
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
Values for \(A, B, C, D,\) and \(E\) are to be selected from \(\{1, 2, 3, 4, 5, 6, 7, 8\}\) without replacement, where \(E\) represents a horizontal shift. Determine how many ways are there to make such choices so that the two curves \(y = Ax^2 + B\) and \(y = (C(x+E))^2 + D\) intersect.
A) 36
B) 48
C) 50
D) 60
E) 72

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