
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
In a right triangle with base \(b\), height \(h\), hypotenuse \(c\), and the radius of the inscribed circle \(r\), find the ratio of the area of the circle to the area of the triangle.

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