
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
Consider a square and a right triangle. The perimeter of the square is 80, and the triangle has a height of 72 against the vertical side. If both the square and the triangle have the same area, find the base length of the triangle.

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