
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
On the complex plane, the points corresponding to the conditions $\left\{\begin{array}{l}0 \leqslant \arg (z-1) \leqslant \frac{\pi}{4}, (\operatorname{Re}(z) \text{ represents the real part of } z) \end{array}\right.$ and $\operatorname{Re}(z) \leqslant 2$ form a region with an area of .___

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