
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 the complex number \( z = 2 \cos^2 \theta + \mathrm{i} + (\sin \theta + \cos \theta)^2 \mathrm{i} \), where \( \theta \in \left[ 0, \frac{\pi}{2} \right] \), find the maximum and minimum values of \( |z| \).

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