
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 line $l$ has a y-intercept of $-2$ and is perpendicular to the line $x-2y-1=0$.
(1) Find the equation of line $l$;
(2) Suppose line $l$ intersects the two coordinate axes at points $A$ and $B$, and $\triangle OAB$ is inscribed in circle $C$, find the general equation of circle $C$.

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