
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
The radius of the circumcircle of $\triangle ABC$ is 1, with the center at $O$, and it is given that $2\overrightarrow{OA} + \overrightarrow{AB} + \overrightarrow{AC} = \overrightarrow{0}$. If $|\overrightarrow{OA}| = |\overrightarrow{AB}|$, then $\overrightarrow{CA} \cdot \overrightarrow{CB} = \boxed{\text{\_\_\_\_\_\_}}$.

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