
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
Suppose $A, B, C,$ and $D$ are distinct integers chosen from the set $\{1, 2, 3, 4, 5, 6\}$. Determine how many ways there are to select these values such that the curves $y = Ax^2 + Bx + 1$ and $y = Cx^2 + Dx + 1$ intersect.

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