
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
Abby has an isosceles triangle with a base of 10 inches and a height of 12 inches. She wants to divide this triangle into ten equal-area segments by drawing lines from the apex to points along the base. What is, to the nearest hundredth of an inch, the greatest perimeter among these ten segments?

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