
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 $PQR,$ point $G$ is on $\overline{PQ}$ such that $PG:GQ = 4:1,$ and point $H$ is on $\overline{QR}$ such that $QH:HR = 4:1.$ If lines $GH$ and $PR$ intersect at $J,$ find the ratio $\frac{GH}{HJ}.$

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