
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

The positive integers \(a, b, c, d\) satisfy \(a > b > c > d\), \(a + b + c + d = 2010\), and \(a^2 - b^2 + c^2 - d^2 = 2010\). How many different sets of possible values of \((a, b, c, d)\) are there?

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