
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 points $P,$ $Q,$ and $R$ are represented by the complex numbers $z,$ $(1 - i) z,$ and $2z,$ respectively, where $|z| = 1.$ When $P,$ $Q,$ and $R$ are not collinear, let $S$ be the fourth vertex of the parallelogram $PQSR.$ What is the maximum distance between $S$ and the origin of the complex plane?

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