
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 suggests that years ending in double zeroes will be considered leap years only if, when divided by 800, the year leaves a remainder of 200 or 600. How many leap years, under this new proposal, occur between the years 2000 and 5000 that end in double zeroes?

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