
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 spherical balls, each with a diameter of 8 cm. In one crate (Crate X), balls are stacked in vertical rows with each ball directly above the lower one. The other crate (Crate Y) uses a staggered arrangement such that each ball in one row is nestled in the spaces formed by the balls in the row below. Crate X and Crate Y both contain exactly 150 balls. Determine the positive difference in the total heights (in cm) of the stacked balls in the two crates.

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