
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 that the radius of circle O is 1, and points A, B, C are moving points on circle O, satisfying $\angle AOB=120^\circ$, $\overrightarrow{OC} = m\overrightarrow{OA} + n\overrightarrow{OB}$ ($m, n \in \mathbb{R}$), then the range of values for $m^4+n^4$ is \_\_\_\_\_\_.

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