
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 of length 30 cm and 40 cm. Find the lengths of the legs of the triangle.

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