
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
Given the length of the body diagonal of a cuboid is 10, and the length of its orthogonal projection on one face of the cuboid is 8, find the maximum volume of this cuboid.

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