
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
Three identical cylindrical pipes, each with a diameter of 12 cm, are packed in a triangular pattern within a crate, similar to the arrangement in Crate B. Given the triangular packing and the increase in pipe diameter, determine the height, \( h \), of a pile consisting of 5 pipe layers, where the pipes in all layers beyond the first are placed in the triangular gaps formed by the pipes in the layer directly below.

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