
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 point on the hypotenuse, equidistant from both legs, divides the hypotenuse into segments with lengths of 30 and 40. Find the lengths of the legs of the triangle.

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