
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 the planar vectors $\overrightarrow{PA}, \overrightarrow{PB}$ that satisfy $|\overrightarrow{PA}| = |\overrightarrow{PB}| = 1, \overrightarrow{PA} \cdot \overrightarrow{PB} = -\frac{1}{2}$, if $|\overrightarrow{BC}| = 1$, find the maximum value of $|\overrightarrow{AC}|$.

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