
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
For how many positive integers \( n \le 500 \) is
\[
\left\lfloor \frac{497}{n} \right\rfloor + \left\lfloor \frac{498}{n} \right\rfloor + \left\lfloor \frac{499}{n} \right\rfloor
\]
not divisible by \(4\)? Recall that \( \lfloor x \rfloor \) represents the greatest integer less than or equal to \( x \).
A) 10
B) 11
C) 12
D) 13
E) 14

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