
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
Determine the number of ways to color each integer from $2$ to $12$ with one of three colors (red, green, or blue), ensuring each integer is colored differently from each of its proper divisors.
**A)** 1920
**B)** 2500
**C)** 3495
**D)** 5832
**E)** 6250

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