
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
In the rectangular coordinate system with origin $O$, point $A(4,-3)$ is the right-angle vertex of $\triangle OAB$, and it is known that $|AB|=2|OA|$, with the $y$-coordinate of point $B$ being greater than $0$.
1. Find the coordinates of point $B$.
2. Find the equation of the circle that is symmetric to the circle $x^2-6x+y^2+2y=0$ about the line $OB$.

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