
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 proposes that years ending in double zeroes are considered leap years only if the year leaves a remainder of 300 or 700 when divided by 1300. Determine the number of leap years that end in double zeroes between 2000 and 5000 under this new rule.

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