
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
Given $A, B, C,$ and $D$ are to be selected from $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ without replacement, find the number of ways to make choices for $A, B, C,$ and $D$ such that the curves $y = Ax^2 + B$ and $y = Cx^2 + D$ intersect, and the y-intercept of the first curve is greater than the y-intercept of the second curve.

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