
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 of integers $N$ between 1 and 1985 such that the improper fraction $\frac{N^2+3}{N+2}$ is not in lowest terms.
A) 280
B) 282
C) 283
D) 285

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