
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 $a$, $b$, and $c$ are all real numbers, and satisfy $\left(2-a\right)^{2}+\sqrt{{a^2}+b+c}+|{c+8}|=0$, and $ax^{2}+bx+c=0$, find the value of the algebraic expression $3x^{2}+6x+1$.

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