
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
The angle between vectors $\overrightarrow{\mathrm{OA}}$ and $\overrightarrow{\mathrm{OB}}$ is $\theta$, with $|\overrightarrow{\mathrm{OA}}|=2$ and $|\overrightarrow{\mathrm{OB}}|=1$. Given $\overrightarrow{\mathrm{OP}} = \mathrm{t} \overrightarrow{\mathrm{OA}}$ and $\overrightarrow{\mathrm{OQ}} = (1-\mathrm{t}) \overrightarrow{\mathrm{OB}}$, and $|\overrightarrow{PQ}| = f(t)$ attains its minimum value at $t = t_0$, where $0 < t_0 < \frac{1}{5}$, determine the range of $\theta$.

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