
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
In triangle $ABC$, the radius of the circumscribed circle is $1$, the center of the circle is $O$, and it is given that $2\vec{OA}+\vec{AB}+\vec{AC}=\vec{0}$, $|\vec{OA}|=|\vec{AB}|$. Find the value of $\vec{CA} \cdot \vec{CB}$.

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