
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
A line passing through the point $(4,0)$ with a slope of $-\frac{\sqrt{3}}{3}$ intersects the circle ${x}^{2}+{y}^{2}-4x=0$ at points $A$ and $B$, with $C$ being the center of the circle. Find the value of $\overrightarrow{AB}\cdot \overrightarrow{AC}$.

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