
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 identical cylindrical pipes, each with a diameter of 12 cm, are stacked in a crate. The first three pipes are arranged touching each other at the base in a triangular pattern, and the fourth pipe rests symmetrically on top of the first three. Determine the total height, $h$, from the base to the top of the stack.

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