
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 points A $(2,0)$ and B $(-1,\sqrt{3})$ are fixed points on the circle $x^2+y^2=4$, line passing through B intersects the circle at another point C. When the area of $\triangle ABC$ is maximized, find the equation of line BC.

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