
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
A parabola $Q$ with a focus at $(0,0)$ goes through the points $(2,5)$ and $(-2,-5)$. Determine for how many points $(x,y)\in Q$ with integer coordinates is it true that $|x + 6y|\leq 500$?
A) 38
B) 40
C) 42
D) 44
E) 46

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