
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
An odd six-digit number is called "just cool" if it consists of digits that are prime numbers, and no two identical digits are adjacent. How many "just cool" numbers exist?

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