
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 $l: kx - y - 4k + 1 = 0$ is intersected by the circle $C: x^2 + (y + 1)^2 = 25$ and the length of the chord is an integer, determine the number of lines $l$ that satisfy the condition.

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