
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 non-collinear unit vectors \(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\) in a plane, satisfying \(\boldsymbol{a} + \boldsymbol{b} + \boldsymbol{c} = \boldsymbol{0}\). If \(0 \leqslant t \leqslant 1\), what is the range of the expression \(|-2\boldsymbol{a} + t\boldsymbol{b} + (1-t)\boldsymbol{c}|\)?

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