
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 a complex number $z$ that satisfies $|z|= \sqrt{2}$, and the imaginary part of $z^{2}$ is $2$.

(1) Find the complex number $z$;

(2) Let $A$, $B$, and $C$ be the points corresponding to $z$, $z^{2}$, and $z-z^{2}$ in the complex plane, respectively. Find the area of $\triangle ABC$.

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