
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
Two identical rectangular crates are packed with cylindrical pipes each having a diameter of 12 cm, using different methods. Both crates are packed with 200 pipes each. Crate A uses a direct column formation above each other, while Crate B uses a staggered row formation where every row starts with a half-diameter offset to the previous row.

Calculate the positive difference in the total heights (in cm) of the packing between the two crates.

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