
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
Let \( A, B, C \) be distinct points on a circle \( \odot O \) such that \(\angle AOB = 120^\circ\). Point \( C \) lies on the minor arc \( \overparen{AB} \) (and \( C \) is not coincident with \( A \) or \( B \)). If \(\overrightarrow{OC} = \lambda \overrightarrow{OA} + \mu \overrightarrow{OB}\) (\( \lambda, \mu \in \mathbb{R} \)), what is the range of values for \( \lambda + \mu \)?

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