
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 $\triangle PQR,$ where $PQ=PR=17$ and $QR=15.$ Points $G,H,$ and $I$ are on sides $\overline{PQ},$ $\overline{QR},$ and $\overline{PR},$ respectively, such that $\overline{GH}$ and $\overline{HI}$ are parallel to $\overline{PR}$ and $\overline{PQ},$ respectively. What is the perimeter of parallelogram $PGHI$?

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