
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 $z\in Z$, and the point corresponding to $z$ in the complex plane is $Z$. If $z$ satisfies the following conditions: $1 \lt |z| \lt 2$, then the area of the geometric shape corresponding to the set of points $Z$ is ______. (Keep the calculation result as $\pi$)

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