
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 $12\sqrt{2}$ units each and slant edges of length 15 units each is cut by a plane that is parallel to its base and 5 units above its base. What is the volume, in cubic units, of the new (smaller) pyramid that is cut off by this plane?

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