
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 aims to designate years that end in double zeroes as leap years only if they leave a remainder of 300 or 500 when divided by 800. Using this proposal, how many leap years will there be that end in double zeroes between the years 2050 and 4050?

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