
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
Two parabolas have equations $y = 2x^2 + ax + b$ and $y = 2x^2 + cx + d$, where $a, b, c,$ and $d$ are integers, each chosen independently from the set $\{-3, -2, -1, 0, 1, 2\}$. What is the probability that the parabolas will have at least one point in common?
A) $\frac{1}{2}$
B) $\frac{25}{36}$
C) $\frac{5}{6}$
D) $\frac{31}{36}$
E) $1$

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