
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 $\triangle ABC$ with $AB = 2$, $AC = 1$, and $\angle BAC = 120^\circ$, $O$ is the circumcenter of $\triangle ABC$. If $\overrightarrow{AO} = \lambda \overrightarrow{AB} + \mu \overrightarrow{AC}$, find $\lambda + \mu$.

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