
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
A natural number is considered "cool" when each of its digits is greater than any of the other digits to its left. For example, 3479 is cool, while 2231 is not. How many cool numbers are there between 3000 and 8000?

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