
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 filled with cylindrical pipes arranged in two different packing methods. Each pipe has a diameter of 8 cm. In the first method (Crate A), the pipes are arranged directly on top of each other in rows. In the second method (Crate B), the pipes are arranged in a staggered (hexagonal) packing. A new top "layer" has been added to both packing styles - this layer only spans half the length of the crate and contains half the number of pipes that fit in a single full horizontal row. After filling each crate with 160 pipes (plus the additional top layer), what is the positive difference in the total heights (in cm) of the two packings?

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