
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
Let $g(x)$ be a monic polynomial such that $g(0) = 6$ and $g(2) = 18$. If $g(x)$ is of degree 2, find $g(x)$, expressing your answer as $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers.

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