
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 an equilateral triangle $\triangle ABC$, point $P$ is on segment $AB$ with $\overrightarrow{AP} = \lambda \overrightarrow{AB}$, where $0 \leqslant \lambda \leqslant 1$.

(1) If the side length of the equilateral triangle is 6, and $\lambda = \frac{1}{3}$, find $|\overrightarrow{CP}|$.

(2) If $\overrightarrow{CP} \cdot \overrightarrow{AB} \geqslant \overrightarrow{PA} \cdot \overrightarrow{PB}$, find the range of values for $\lambda$.

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