
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 six red cards numbered $1$ through $6$ and six blue cards numbered $3$ through $8$. She stacks the cards ensuring that the colors alternate, and that the number on each red card divides evenly into the number on each neighboring blue card except for two specific blue cards which allow a prime divisor outside the sequence. What is the sum of the numbers on the middle four cards in a valid arrangement?
A) 16
B) 18
C) 19
D) 21
E) 22

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