
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
Find all integers \( k \) such that the quadratic equation in \( x \), \( kx^2 - 2(3k - 1)x + 9k - 1 = 0 \), has at least one integer root.

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