Tao te Ching: 61

A big country may be compared to the lower part of a river.
It is the converging point of the world;
It is the female of the world.
The female always overcomes the male by tranquility,
And by tranquility she is underneath..
A big state can take over a small state if it places itself below the small state;
And the small state can take over the a big state if it places itself below the big state.
Thus some, by placing themselves below, take over (others),
And some, by being (naturally) low, take over (other states).
After all, what a big states wants is but to annex and herd others,
And what a small state wants i merely to join and serve others.
Since both and big and small states get what they want,
The big state should place itself low.

So little states want to serve big empires. That sounds like something a big country uses as a justification for annexation to me, but I live in a big state in modern times. There isn't much danger of physical annexation where the United States is concerned. Economic and cultural annexation seems more likely, and the river metaphor stays there.

If a state (which is really an analogy for a person) is at the mouth of the river, it is as the lowest. It is also better able to use wu-wei. After all, how much less action can one take than to be the gate through which all others pass? Your views and beliefs are naturally transmitted by virtue of being the gate.

The important part is that tranquility and passivity can overcome or outlast the more energetic actions of the country on top.

Ultimately, Lao Tzu is advocating passivity to get what you want while letting others expend their energy.