
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A right triangle has a hypotenuse of length $c$ and an altitude from the right angle to the hypotenuse of length $h$. A rectangle is inscribed in the triangle such that one of its longer sides lies along the hypotenuse of the triangle and the opposite side touches the altitude. If the height of the rectangle is $x$, find the area of the rectangle.

Present the answer in LaTex format: \boxed{Your answer}
user