
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 $P, Q,$ and $R$ represent the points on the complex plane with complex numbers $z, (2+i)z,$ and $3\overline{z}$ respectively, where $|z| = 1$. If $P, Q,$ and $R$ are not collinear, and $S$ is the fourth vertex of the parallelogram $PQRS$, find the minimum distance between $S$ and the origin.

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