
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 \( z \in \mathbf{C} \) such that \( |z - \mathrm{i}| \leq 1 \). Define \( A = \operatorname{Re}(z) \left( |z - \mathrm{i}|^2 - 1 \right) \). Find the maximum and minimum values of \( A \).

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