
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 \(0 < \lambda < 1\). The plane vectors \(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\) satisfy \(|\boldsymbol{a}| = 1\), \(|\boldsymbol{b}| = 2\), \(|\boldsymbol{c}| = 3\). 

If \(\boldsymbol{b} \cdot \boldsymbol{c} = 0\), find the set of all values that \(|\boldsymbol{a} - \lambda \boldsymbol{b} - (1 - \lambda) \boldsymbol{c}|\) cannot take.

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