
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 called a leap year if it is either divisible by 4 but not divisible by 100, or divisible by 400. Hence, the years 2000, 2004, and 2400 are leap years while the years 2006, 2100, and 2200 are not. Find the number of leap years between 2000 and 4000 inclusive.

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