
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
Sally has four red cards numbered $1$ through $4$, three blue cards numbered $2$ through $4$, and three green cards numbered $5$ through $7$. She wants to stack these cards such that the colors alternate (red, blue, green in any order) and such that the number on each card perfectly divides the number on each neighboring card of a different color. How many valid stacking sequences can Sally make?
A) 3
B) 4
C) 5
D) 6
E) 7

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