
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 4.5 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?

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