
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

The polynomial \( G(x) \) with real coefficients takes the value 2022 at exactly five distinct points \( x_{1}<x_{2}<x_{3}<x_{4}<x_{5} \). It is known that the graph of the function \( y=G(x) \) is symmetric with respect to the line \( x=-7 \).

(a) Find \( x_{1}+x_{3}+x_{5} \).

(b) What is the minimum degree that \( G(x) \) can have?

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