
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
How many ways are there to paint each of the integers $2, 3, \cdots, 10$ either red, green, or blue so that each number has a different color from each of its proper divisors, and no two consecutive numbers share the same color?
A) 64
B) 96
C) 128
D) 192
E) 216

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