
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
50 balls numbered from 1 to 50 are arranged in a row and are colored as follows: (1) Color 2 balls; (2) The difference in the numbers of the two colored balls is greater than 2. If in one coloring method, the numbers of the two colored balls differ from those in another coloring method, these two coloring methods are considered "different." How many different coloring methods are there?

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