
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
Consider an isosceles triangle with a vertex angle \( \theta \) and a constant height \( h \). A rectangle is inscribed in this triangle such that one side of the rectangle lies along the base of the triangle. The altitude of the rectangle from the base to the opposite side is \( x \). Find the maximum possible area of the rectangle as a function of \( x \), \( h \), and \( \theta \).

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