In the process of river capture, the head streams of the weaker river are diverted into the powerful river. This is a true statement. River capture occurs when the headwaters, or the beginning part, of one river flow into another river. The weaker river is essentially "captured" by the more powerful river.

The reason given for this assertion is that the powerful river erodes its valley steadily. This is also true. A powerful river has the ability to erode its surrounding valley over time. The constant erosion results in the creation of a deeper and wider channel, which can attract the head streams of a weaker river.

Therefore, both the assertion and the reason are true statements. Additionally, the reason correctly explains why the assertion is true. As the more powerful river erodes its valley, it becomes an attractive pathway for the head streams of a weaker river to flow into. This process is known as river capture.

In conclusion, option 1 is the correct answer as both the assertion (A) and the reason (R) are true, and the reason is a correct explanation of the assertion.