
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 \( z, 2iz, \) and \( (1 - i)\overline{z}, \) 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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