
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
Four cylindrical pipes, each with diameter $12\text{ cm}$, are stacked in a crate to form a square-based pyramid. The bottom layer consists of three pipes each touching the other two, and the fourth pipe rests on top at the points where the first three touch. Determine the total height, $h$, of this stack of pipes.

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