
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 the formulas provided:

\[ 
S_{\triangle A O B} = \frac{1}{2} \operatorname{Im}\left(\overline{t_{1}} t_{2}\right) = \frac{1}{4 \mathrm{i}}\left(\overline{t_{1}} t_{2} - t_{1} \overline{t_{2}}\right) 
\]
\[ 
\sin \angle A O B = \frac{\operatorname{Im}\left(\overline{t_{1} t_{2}}\right)}{\left|t_{1} t_{2}\right|} = \frac{\overline{t_{1} t_{2}} - t_{1} \overline{t_{2}}}{2 \mathrm{i}\left|t_{1} t_{2}\right|},
\]
It is assumed that we rotate counterclockwise from \(OA\) to \(OB\).

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