
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
A circle with its center at the vertex of the right angle of a right triangle and a radius equal to the length of the shorter leg divides the hypotenuse into segments of 98 and 527 (starting from the shorter leg). Find the lengths of the legs.

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