
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
Through the point (2, 0) draw a line $l$ that intersects the circle $x^2+y^2=2$ at points $A$ and $B$. Let $O$ be the origin of the coordinate system. When the area of $\Delta AOB$ is maximized, the slope of the line $l$ is ______.

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