
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 that AB is a chord on the unit circle, and P is a moving point on the unit circle, let $f(\lambda) = |\overrightarrow{BP} - \lambda \overrightarrow{BA}|$ be the minimum value M. If the maximum value of M, $M_{\text{max}}$, satisfies $M_{\text{max}} \geq \frac{3}{2}$, then the range of values for $|\overrightarrow{AB}|$ is \_\_\_\_\_\_.

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