
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 $2, 3, \cdots, 11$ either red, green, or blue such that:
1. Each number has a different color from each of its proper divisors.
2. Numbers divisible by $5$ must also consider a different color than their immediate predecessor.
A) 864
B) 1080
C) 1296
D) 1458
E) 1620

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