I am no expert in ancient Chinese. This is a wild guess at best:
无 /woo/: without.
为 /wei/: strife, forceful means, exertion.
无为/woo wei/: without imposing; without the use of forceful means; without bending others to your will; without strife; without struggle; without exertion.
而: grammatical connector, similar to "to".
治: to rule, to manage.
无为而治: to rule without imposing; to rule without the use of forceful means; to rule without bending others to your will; to rule without strife; to rule without forceful exertion.
If this aphorism advocates ruling in the manner of a lighthouse instead of a border collie, then "without acting" or "doing nothing" is definitely not what it means. Yet, lighthouses have no effect on sheep, and it was sheep themselves who make the border collie efficient. Where this piece of aphorism applies, the people must be very reasonable; it is no surprise that a sheep culture also produces ruthless tyrants.
"Action without acting" is probably a mystified translation. Misinterpretations of ancient Chinese by modern yet pre-scientific Chinese scholars have been a major source of Chinese muddleheadedness. It is possible that the Chinese population experienced a degenerating process around 210BC similar to that of the ancient Greeks.
Evidence that supports my interpretation:
In the Art of War, there is a sentence 胜可知，而不可为 (victory can be foreseen but cannot be achieved by strife) where 为(wei) means "by strife","by forceful means" or "by strenuous, deliberate exertions" or "by struggle."
Bertrand Russell in his Problem of China quoted a Taoist fable that captured a similar naturalistic spirit:
Perhaps it is not clear what I mean by "the mechanistic outlook." I mean something which exists equally in Imperialism, Bolshevism and the Y.M.C.A.; something which distinguishes all these from the Chinese outlook, and which I, for my part, consider very evil. What I mean is the habit of regarding mankind as raw material, to be moulded by our scientific manipulation into whatever form may happen to suit our fancy. The essence of the matter, from the point of view of the individual who has this point of view, is the cultivation of will at the expense of perception, the fervent moral belief that it is our duty to force other people to realize our conception of the world. The Chinese intellectual is not much troubled by Imperialism as a creed, but is vigorously assailed by Bolshevism and the Y.M.C.A., to one or other of which he is too apt to fall a victim, learning a belief from the one in the class-war and the dictatorship of the communists, from the other in the mystic efficacy of cold baths and dumb-bells. Both these creeds, in their Western adepts, involve a contempt for the rest of mankind except as potential converts, and the belief that progress consists in the spread of a doctrine. They both involve a belief in government and a life against Nature. This view, though I have called it mechanistic, is as old as religion, though mechanism has given it new and more virulent forms. The first of Chinese philosophers, Lao-Tze, wrote his book to protest against it, and his disciple Chuang-Tze put his criticism into a fable:—
Horses have hoofs to carry them over frost and snow; hair, to protect them from wind and cold. They eat grass and drink water, and fling up their heels over the champaign. Such is the real nature of horses. Palatial dwellings are of no use to them.
One day Po Lo appeared, saying: "I understand the management of horses."
So he branded them, and clipped them, and pared their hoofs, and put halters on them, tying them up by the head and shackling them by the feet, and disposing them in stables, with the result that two or three in every ten died. Then he kept them hungry and thirsty, trotting them and galloping them, and grooming, and trimming, with the misery of the tasselled bridle before and the fear of the knotted whip behind, until more than half of them were dead.
The potter says: "I can do what I will with clay. If I want it round, I use compasses; if rectangular, a square."
The carpenter says: "I can do what I will with wood. If I want it curved, I use an arc; if straight, a line."
But on what grounds can we think that the natures of clay and wood desire this application of compasses and square, of arc and line? Nevertheless, every age extols Po Lo for his skill in managing horses, and potters and carpenters for their skill with clay and wood. Those who govern the Empire make the same mistake.
Although Taoism, of which Lao-Tze was the founder and Chuang-Tze the chief apostle, was displaced by Confucianism, yet the spirit of this fable has penetrated deeply into Chinese life, making it more urbane and tolerant, more contemplative and observant, than the fiercer life of the West.
Source: Russell, Bertrand. Problem of China, 1922.