
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 year is considered "super lucky" if there are at least two different dates in the year, where the date when written in the form month/day/year, has the product of the month times the day equal to the last two digits of the year. Determine the first "super lucky" year after 2000.

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