
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
In $\triangle ABC$, $CA=2$, $CB=6$, and $\angle ACB = 60^{\circ}$. Suppose point $O$ is on the angle bisector of $\angle ACB$, satisfying $\overrightarrow{OC} = m \overrightarrow{OA} + n \overrightarrow{OB}$ with $m, n \in \mathbf{R}$, and $-\frac{1}{4} \leq n \leq -\frac{1}{20}$. Determine the range of $|\overrightarrow{OC}|$.

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