
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 planar vectors $\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}$ satisfying $|\boldsymbol{a}| = 1$, $|\boldsymbol{b}| = 2$, $|\boldsymbol{c}| = 3$, and $0 < \lambda < 1$, if $\boldsymbol{b} \cdot \boldsymbol{c} = 0$, then find the values that cannot be taken by $|\boldsymbol{a}-\lambda \boldsymbol{b}-(1-\lambda) \boldsymbol{c}|$.

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