
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
Consider two parabolas with equations $y = x^2 + ax + bx + c$ and $y = x^2 + dx + ex + f$ where $a, b, c, d, e,$ and $f$ are integers, each independently chosen by rolling a fair six-sided die. Find the probability that these parabolas have at least one point in common.

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