
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
Circle $C: x^{2}+\left(y-2\right)^{2}=16$ is symmetric with respect to the line $ax+by-12=0$. Point $S$ lies on the line $y+b=0$, and two tangent lines $SA$ and $SB$ are drawn from point $S$ to circle $C$, with tangent points $A$ and $B$ respectively. The line $AB$ must pass through a fixed point, and the coordinates of the fixed point are ______.

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