
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
Points \( A, B, \) and \( C \) are distinct points on circle \( O \), with \(\angle AOB = 120^\circ\). Point \( C \) lies on the minor arc \( \overset{\frown}{AB} \) (not coinciding with points \( A \) or \( B \)). Given that \(\overrightarrow{OC} = \lambda \overrightarrow{OA} + \mu \overrightarrow{OB} (\lambda, \mu \in \mathbb{R})\), determine the range of values of \(\lambda + \mu\).

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