
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
What is the area of the region in the complex plane consisting of all points  $z$  satisfying both  $|\tfrac{1}{z}-1|<1$  and  $|z-1|<1$ ? ( $|z|$  denotes the magnitude of a complex number, i.e.  $|a+bi|=\sqrt{a^2+b^2}$ .)

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