
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 three-digit number is called a "cool number" if there is a digit in one of its places that is half the product of the other two digits. A three-digit number is called a "super cool number" if such digits appear in two or three of its places. How many different "super cool numbers" exist? (Zero is not allowed in the digits of "cool" and "super cool" numbers).

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