
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
Given that an imaginary number \( z \) satisfies \( w = z + \frac{1}{z} \) where \( w \) is a real number, and \(-1 < w < 2\). Let \( u = \frac{1 - z}{1 + z} \). What is the minimum value of \( \left|w - u^{2}\right| \)?

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