
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 the vectors $\overrightarrow{a} = (1, \sqrt{3})$ and $\overrightarrow{b} = (-2, 0)$:
1. Calculate $|\overrightarrow{a} - \overrightarrow{b}|$;
2. Find the angle between the vector $\overrightarrow{a} - \overrightarrow{b}$ and $\overrightarrow{a}$;
3. For $t \in \mathbb{R}$, determine the range of values for $|\overrightarrow{a} - t\overrightarrow{b}|$.

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