
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 Cartesian coordinate system xOy, given the equation of circle C is $x^2 + y^2 - 8x + 15 = 0$. If there is at least one point on the line $y = kx - 2$ that is tangent to the circle with center C and radius 1, then the maximum value of $k$ is __________.

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