
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
Let \( Q \) be a parabola with focus at \( (0,2) \) that passes through the points \( (5,4) \) and \( (-5,-4) \). Determine how many points \( (x,y) \) on \( Q \) with integer coordinates satisfy \( |5x + 4y| \leq 1200 \).
**A)** 616
**B)** 617
**C)** 618
**D)** 619
**E)** 620

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