
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 center of a semicircle, inscribed in a right triangle such that its diameter lies on the hypotenuse, divides the hypotenuse into segments of 30 and 40. Find the length of the arc of the semicircle that is enclosed between the points where it touches the legs.

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