
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 $PQR$ has side lengths $PQ=7$, $QR=8$, and $PR=9$. Two ants start simultaneously from $P$ and crawl along the perimeter of the triangle in opposite directions at the same speed. They meet at point $S$. What is $QS$?

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