
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
\(\triangle P N R\) has side lengths \(P N=20, N R=18\), and \(P R=19\). Consider a point \(A\) on \(P N\). \(\triangle N R A\) is rotated about \(R\) to \(\triangle N^{\prime} R A^{\prime}\) so that \(R, N^{\prime}, and P\) lie on the same line and \(A A^{\prime}\) is perpendicular to \(P R\). Find \(\frac{P A}{A N}\).

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