
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 used to pack cylindrical cans using different methods. Each can has a diameter of 12 cm. One crate packs the cans side-by-side in straight rows, filling up 15 rows with 12 cans per row. Another packs them in a staggered pattern, where each new row starts at the midpoint of two cans from the previous row, filling up 13 rows with 11 cans in the first row and subsequent rows alternating between 10 and 11 cans. Calculate the positive difference in the total heights (in cm) of the two packing methods after they are fully packed.

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