
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
A box has the shape of a rectangular block with dimensions $102 \mathrm{~cm}, 255 \mathrm{~cm}$, and $170 \mathrm{~cm}$. We want to store in this box the smallest possible number of small cubes with integer edges, in such a way as to completely fill the box.

(a) What is the edge length of each cube?

(b) How many cubes will be needed?

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