
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 $O$ is a point inside $\triangle ABC$, and $\vec{OA} + \vec{OB} + \vec{OC} = 0$, $\vec{AB} \cdot \vec{AC} = 2$, with $\angle BAC = 60^\circ$, find the area of $\triangle OBC$.

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