
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
Let the sides of a right rectangular prism $P$ be $a, b, c$ (where $a \leq b \leq c$) with $b=2023$. A plane parallel to one of the faces cuts $P$ into two smaller prisms, one of which is similar to $P$, and both have nonzero volumes. Find the number of ordered triples $(a, b, c)$ for which this plane exists.

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