
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
Define: If a positive integer can be expressed as the difference of the squares of two positive integers $m$ and $n$, and $m-n \gt 1$, then this positive integer is called a "wise superior number." For example, $16=5^{2}-3^{2}$, $16$ is a wise superior number, and it can be studied using $m^{2}-n^{2}=\left(m+n\right)\left(m-n\right)$. If the wise superior numbers are arranged in ascending order, then the $3$rd wise superior number is ______; the $23$rd wise superior number is ______.

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