
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 three unit vectors $\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}$ in a plane that are not collinear and satisfy $\boldsymbol{a} + \boldsymbol{b} + \boldsymbol{c} = \mathbf{0}$. If $0 \leq t \leq 1$, what is the range of values of $|-2 \boldsymbol{a} + t \boldsymbol{b} + (1-t) \boldsymbol{c}|$?

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