
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 two non-parallel vectors $\overrightarrow{a},\;\overrightarrow{b}$ such that $|\overrightarrow{a}|=1$ and $\overrightarrow{a}\cdot\overrightarrow{b}=\sqrt{3}$. If for any $t\in \mathbb{R}$, $|\overrightarrow{b}-t\overrightarrow{a}|\geq 2$ holds, then the minimum value of $|\overrightarrow{b}|$ is ______.

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