
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
Let the points \( A(1,1), B, \) and \( C \) be on the ellipse \( x^{2} + 3y^{2} = 4 \). Find the equation of the line \( BC \) such that the area of \( \triangle ABC \) is maximized.

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