
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
Positive integers \(p\), \(q\), \(r\), and \(s\) satisfy \(p > q > r > s\), \(p + q + r + s = 2020\), and \(p^2 - q^2 + r^2 - s^2 = 2020\). Find the number of possible values of \(p\).

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