
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 circumcircle of $\triangle ABC$, denoted as circle $O$ with a radius of $2$, and $\vec{AB} + \vec{AC} = 2\vec{AO}$, $|\vec{AB}| = |\vec{AO}|$, find the value of $\vec{CA} \cdot \vec{CB}$.

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