
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 a line passing through point $P(1,1)$, which divides the circular region $\{(x, y) | x^2 + y^2 \leq 4\}$ into two parts, how should the line be drawn so that the difference in area between the two parts is maximized? Find the equation of this line.

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