
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
Given \(a, b, c, d\) (where \(a < b < c < d\)) are positive integers not exceeding 2012, and they form an arithmetic sequence in this order. How many different sets of possible values of \((a, b, c, d)\) are there?

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