
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
\(ABCD\) is a square-based pyramid with base \(ABCD\) and apex \(E\). Point \(E\) is directly above point \(A\), with \(AE = 1024\) units and \(AB = 640\) units. The pyramid is sliced into two parts by a horizontal plane parallel to the base \(ABCD\), at a height \(h\) above the base. The portion of the pyramid above the plane forms a new smaller pyramid. For how many integer values of \(h\) does the volume of this new pyramid become an integer?

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