
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 rectangular prism $P$, a rectangular parallelpiped, has sides of integral length $a, b, c,$ following $a\leq b\leq c$. A plane, parallel to one of the faces of $P$, divides $P$ into two prisms, each prism being similar to $P$, but with different volumes. If $b = 2023$, determine the number of ordered triples $(a, b, c)$ that allow for such a division.

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