
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
C is the complex numbers. \( f : \mathbb{C} \to \mathbb{R} \) is defined by \( f(z) = |z^3 - z + 2| \). What is the maximum value of \( f \) on the unit circle \( |z| = 1 \)?

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