
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 distinct quadratic polynomials \( f(x) \) and \( g(x) \), whose leading coefficients are equal to one. It is known that \( f(1) + f(10) + f(100) = g(1) + g(10) + g(100) \). For which \( x \) is the equality \( f(x) = g(x) \) satisfied?

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