
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 two different methods. Both crates start with a row of $10$ pipes and continue stacking in different configurations. Crate A stacks the pipes directly above each other, while Crate B arranges them in a staggered pattern. Determine the positive difference in the total heights (in cm) of the two packings after filling each crate with 200 pipes.

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