Strength and Power are two different things

Most of the time riders do not know the difference between Strength and Power.
Power is Force (strength) * velocity. So, power depends not only on the amount of force you are able to apply to the pedals but also on how fast you turn those pedals when you apply that force.
In fact, the best power is the best combination between the amount the force applied and the velocity you are able to produce applying that specific amount of force.

Low power can be the result of a huge amount of force at a very slow velocity or of very high velocity and a small amount of force.

The tyranny of the cadence
Do you know that for every rider, for a certain gear on a certain terrain, there is the "perfect" cadence that will provide the best power for the force the rider is able to apply to the pedals when he/she turns them at that specific velocity. If your cadence is higher, you may see your power dropping, because the cadence is too high and the force applied to the pedals decreases.

Therefore, just trying to increase your cadence is not always beneficial, there is that "cadence" threshold, above which your power will drop.

So, when you climb, for example, try the same portion of the climb, different times with different gear ratios, and pick the one that allows you to ride that portion in the shortest time.