
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 equation of circle $\odot C$ is $x^{2}+y^{2}-8x+15=0$. If there exists at least one point on the line $y= kx-2$ (where $k \in \mathbb{R}$) such that the circle with this point as its center and radius 1 has a common point with $\odot C$, what is the maximum value of $k$?

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