
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
The base of a triangle is $a$, and the altitude dropped to the base is $h$. A square is inscribed in the triangle such that one side of the square lies on the base, and two vertices are on the other two sides of the triangle. Find the ratio of the area of the square to the area of the triangle.

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