
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 crates, Crate X and Crate Y, are packed with cylindrical pipes, each with a diameter of 12 cm, using square and hexagonal packing arrangements respectively. Both crates initially contain the same total number of pipes, which is 144. Assuming the crates have sufficient height and the base area accommodates the packing arrangements fully and efficiently, calculate the positive difference in the total heights (in cm) of the two packings.

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