
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
Determine the number $N$ of distinct rational numbers $k$ such that $|k|<50$, and the quadratic equation \[x^2 - kx + 18 = 0\] has at least one integer solution for $x$.
A) 24
B) 36
C) 48
D) 49
E) 50

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