
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
In triangle $ABC,$ $N$ is the midpoint of $\overline{AC},$ $AB = 18,$ and $BC = 24.$ Let $P$ be on $\overline{AB},$ and $Q$ be on $\overline{BC},$ and let $R$ be the intersection of $\overline{PQ}$ and $\overline{BN}.$ If $BP = 2BQ,$ determine the ratio $\frac{PR}{RQ}.$

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