
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
1. Given a complex number $z$ satisfying $|z| = \sqrt{2}$, and the imaginary part of $z^2$ is 2, find the complex number $z$.
2. Find the volume of the solid obtained by rotating the region bounded by the function $f(x) = e^x$, the line $x = 2$, and the two coordinate axes, around the x-axis.

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