
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 proposal states that years ending in double zeroes will be leap years only if the year leaves a remainder of 400 or 600 when divided by 800. Based on this new rule, how many leap years that end in double zeroes will there be between 2000 and 4100?

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