
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 that $\theta$ is an interior angle of a triangle, $i$ is the imaginary unit, and the complex number $z=\cos \theta +i\sin \theta$, and $z^{2}-z$ corresponds to a point on the imaginary axis in the complex plane.<br/>$(1)$ Find the value of $\theta$;<br/>$(2)$ Let $2z$, $\overline{z}$, and $1+z+z^{2}$ correspond to points $A$, $B$, and $C$ in the complex plane, respectively. Find the area of $\triangle ABC$.

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