
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 function $f(x)= \sqrt{3}\sin(\pi-x)\cos(-x)+\sin(\pi+x)\cos\left(\frac{\pi}{2}-x\right)$, a lowest point on its graph is $A$, and the two nearest highest points are $B$ and $C$, respectively. Calculate the dot product $\vec{AB} \cdot \vec{AC}$.

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