
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 that the center of circle $O$ is the origin, the slope is $1$, and the line passing through point $M({\sqrt{2},3\sqrt{2}})$ is tangent to the circle.  
$(1)$ Find the equation of circle $O$;  
$(2)$ The line $l$ passing through $M$ intersects circle $O$ at points $A$ and $B$. If the area of $\triangle OAB$ is $2$, find the equation of line $l$.

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