
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 crates are packed with cylindrical pipes using different methods. Each pipe has a diameter of 15 cm. The first crate (Crate A) is packed in rows of 15 pipes directly one on top of the other, stacked up to 15 rows. The second crate (Crate B) uses a staggered formation packing—similar to the second method in the original problem—with rows alternating between 14 and 15 pipes horizontally. Crate C employs a triangular packing formation scantily addressed before, with 15 pipes in the lowest row, 14 in the second, 13 in the third, continuing in this pattern to the top. Considering the crates have been packed uniformly with equal numbers of pipes significantly, determine the difference in total heights between Crate A and the shorter of Crate B and C.

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