
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 is proposed where a year ending in double zeros will be considered a leap year only if it leaves a remainder of either 300 or 700 when divided by 1000. How many leap years will there be that end in double zeros between 2000 and 5000?

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