
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 $\triangle PQR$, $PQ = 93$, and $PR = 105$. A circle with center $P$ and radius $PQ$ intersects $\overline{QR}$ at points $Q$ and $Y$. Moreover, $\overline{QY}$ and $\overline{YR}$ have integer lengths. Determine the length of $\overline{QR}$.

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