
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 line $l: kx+y-2=0$ (where $k\in \mathbb{R}$) is the axis of symmetry of the circle $C: x^{2}+y^{2}-6x+2y+9=0$, a tangent line to circle $C$ passes through point $A(0,k)$ and touches the circle at point $B$. Find the length of segment $AB$.

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