
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 legs of a right triangle are 6 cm and 8 cm. A circle is drawn through the midpoint of the shorter leg and the midpoint of the hypotenuse, touching the hypotenuse. Find the area of the circle bounded by this circumference.

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