
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
The magnitude of the unit vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ satisfy $\overrightarrow{b} \cdot \overrightarrow{c} = \frac{1}{2}$, then the range of values for $|\overrightarrow{a} - 2\lambda \overrightarrow{b} - (2 - 2\lambda)\overrightarrow{c}| (0 \leqslant \lambda \leqslant 1)$ is \_\_.

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