
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 non-coplanar vectors $\overrightarrow {OA}$ and $\overrightarrow {OB}$ with an angle α between them, $|\overrightarrow {OA}|=1$ and $|\overrightarrow {OB}|=2$. Let $\overrightarrow {OP}$ = (1-t)$\overrightarrow {OA}$ and $\overrightarrow {OQ}$ = t$\overrightarrow {OB}$, where 0 ≤ t ≤ 1. Find the range of the angle α when 0 < t₀ < $\frac{1}{5}$.

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