
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 an isosceles triangle with a base of 10 inches and a height of 12 inches. Divide this triangle into ten pieces that have equal areas by drawing lines from the apex to the base. Find the greatest perimeter among the ten pieces to the nearest hundredth of an inch.

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