
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 $PQR,$ $N$ is the midpoint of $\overline{QR},$ $PQ = 10,$ and $PR = 20.$ Let $J$ be on $\overline{PR},$ and $K$ be on $\overline{PQ},$ and let $L$ be the intersection of $\overline{JK}$ and $\overline{PN}.$ If $PJ = 3PK,$ find $\frac{JL}{LK}.$

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