
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 new rule for identifying leap years proposes that years ending in double zeroes will be leap years only if the year gives a remainder of 300 or 450 when divided by 1200. How many leap years are there that end in double zeroes between the years 2000 and 3000 under this new rule?

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