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

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