
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
The sides $PQ$ and $PR$ of $\triangle PQR$ have lengths 4 and 7, respectively. The length of the median $PM$ is $3 \frac{1}{2}$. Determine the length of $QR$.

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