
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 sets \(M = \{ z \mid |z - 1| \leqslant 1, z \in \mathbf{C} \}\) and \(N = \left\{ z \mid \arg z \geqslant \frac{\pi}{4}, z \in \mathbf{C} \right\}\), find the area of the shape represented by \(M \cap N\) in the complex plane.

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