
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
A section of the graph of $g(x)=ax^2+bx+c$ is shown below. The graph has a vertex at $(2, 1)$ and passes through the point $(0, 9)$. The distance between grid lines on the graph is $1$ unit.

What is the value of $a+2b+c$?

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