
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
The parabola $Q$ has a vertex at $(0, -1)$ and passes through the points $(-3, 4)$ and $(3, 4)$. For how many points $(x, y) \in Q$ with integer coordinates is it true that $|3x - 4y| \leq 1200$?
A) 45
B) 46
C) 47
D) 48
E) 49

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