
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 square base with a perimeter of 32 inches. Its apex is 10 inches away from each of the vertices of the square. What is the height of the pyramid from its peak to the center of its square base, in inches?

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