
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
2000 people are numbered sequentially from 1 to 2000. If the sum of the numbers of some of these people (it can be one person, but it cannot be no one) is a multiple of 5, they are called a "preferred group." Find the number of all possible "preferred groups" that these 2000 people can form.

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