
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 two quadratic polynomials \( f(x) \) and \( g(x) \) both with leading coefficient 1, and each having two real roots. It is also given that \( f(1) = g(2) \) and \( g(1) = f(2) \). Find the sum of the four roots of these two quadratic polynomials.

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