
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 $|Z|= \sqrt {2}$, the imaginary part of $Z^{2}$ is $2$. Let $Z$, $Z^{2}$, $Z-Z^{2}$ correspond to points $A$, $B$, $C$ on the complex plane, respectively. Calculate the area of $\triangle ABC$.

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