
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
Isosceles triangle  $ABC$  with  $AB = AC$  is inscibed is a unit circle  $\Omega$  with center  $O$ . Point  $D$  is the reflection of  $C$  across  $AB$ . Given that  $DO = \sqrt{3}$ , find the area of triangle  $ABC$ .

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