
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 right square pyramid with base edges of length $10\sqrt{2}$ units and slant edges of length 12 units is cut by a plane that is parallel to its base and a quarter of the way up from the base to the apex. What is the volume, in cubic units, of the top, smaller pyramid that is formed by this cut?

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