
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
9000 students participated in a math competition. Their examination numbers are $1000, 1001, 1002, \ldots, 9999$. Xiao Ming found that his examination number is 8210, and his friend Xiao Qiang's examination number is 2180. Their examination numbers are composed of the same digits (in different order), and the difference between their examination numbers is a multiple of 2010. How many such examination numbers (composed of the same digits and the difference being a multiple of 2010) are there in total?

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