
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
Choose values for coefficients $A, B, C, D, E, F$ from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$ without recycling any number so that each letter corresponds to a unique value. Determine the number of ways such that the curves $y=Ax^2+Bx+C$ and $y=Dx^2+Ex+F$ intersect.
A) 3360
B) 5040
C) 6720
D) 10080
E) 20160

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