
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 right pyramid has a triangular base which is an equilateral triangle with a perimeter of 24 inches. Its apex is 10 inches from each vertex of the base. Find the height of the pyramid from its peak to the center of its triangular base.

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