
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
Let $P, Q, R$ be points in the complex plane represented by $z, (3 + 2i)z, -3\overline{z}$ respectively, where $|z| = 1$. Determine the maximum distance from the origin to vertex $S$ of parallelogram $PQRS$ when $P, Q, R$ are not collinear.

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