
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
Find the number of ways to color all natural numbers from 1 to 20 in blue and red so that both colors are used and the product of all red numbers is relatively prime to the product of all blue numbers.

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