
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 the triangle \(PQR\), side \(PQ\) is no more than 9, side \(PR\) is no more than 12. The area of the triangle is at least 54.

Find the median drawn from vertex \(P\).

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