
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 rolls, each having a diameter of 12 cm. Crate A uses a square packing arrangement, while Crate B uses a hexagonal packing arrangement. Both crates are packed such that they contain the same number of rolls. Given that Crate A has 18 rows of 8 rolls each, calculate the positive difference in height (in cm) between the two crates after being packed.

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