
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 \(Q\) has sides of length \(a, b, c\) with \(a \leq b \leq c\). A plane parallel to one of the faces of \(Q\) cuts \(Q\) into two prisms, one of which is similar to \(Q\), and both of which have nonzero volume. Given that \(b = 2023\), determine the number of ordered triples \((a, b, c)\) for which such a plane exists.

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