
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 $R$ be points in the complex plane represented by the complex numbers $z$, $(2+i)z$, and $(1-i)\overline{z}$ respectively, with $|z| = 1$. Assume the points $P$, $Q$, and $R$ are non-collinear. Define $S$ to be the fourth vertex of the parallelogram formed by $PQSR$. Find the maximum distance from $S$ to the origin.

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