
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 triangle has a base of length $b$ and an altitude of length $h$. A rectangle is inscribed in the triangle such that one side of the rectangle lies along the base of the triangle. The length of this side on the base is $y$, and the height of the rectangle inside the triangle is $x$. If the top side of the rectangle remains parallel to the base of the triangle, what is the area of the rectangle?

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