
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
Paul has an isosceles triangle with a base of 10 inches and a height of 12 inches. He wants to cut this triangle into ten pieces, such that each piece has an equal area. The initial cut is made vertically from the apex to the midpoint of the base, creating two right triangles. Each right triangle is then subdivided horizontally into five strips of equal area. What is the greatest perimeter among these ten pieces?

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