
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 plane vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ satisfy $|\overrightarrow{a}|=1$, $|\overrightarrow{b}|=2$, and for all $t\in \mathbb{R}$, $|\overrightarrow{b}+t\overrightarrow{a}| \geq |\overrightarrow{b}-\overrightarrow{a}|$ always holds, determine the angle between $2\overrightarrow{a}-\overrightarrow{b}$ and $\overrightarrow{b}$.

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