
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
On the circle $C:x^2+y^2=4$, there are two points $A(x_1,y_1)$ and $B(x_2,y_2)$. If $|\vec{AB}|=2\sqrt{3}$, then $x_1x_2+y_1y_2=$ ?

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