
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 distinct quadratic polynomials \(f(x)\) and \(g(x)\) with leading coefficients equal to one. It is known that \(f(19) + f(92) = g(19) + g(92)\). For which values of \(x\) is the equality \(f(x) = g(x)\) satisfied?

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