
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 that \(b\) and \(c\) are both integers and \(c < 2000\). If the quadratic equation \(x^{2} - bx + c = 0\) has roots whose real parts are both greater than 1, how many pairs \((b, c)\) satisfy this condition?

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