
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 rectangular base with a perimeter of 40 inches and the length is twice the breadth. Its apex is 15 inches from each vertex of the base. What is the height of the pyramid from its peak to the center of the rectangular base, in inches?

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