
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 portion of the graph of $f(x)=ax^2+bx+c$ passes through the points where the distance between grid lines is $1$ unit. The vertex of the graph is at \((2,3)\), and it passes through the point \( (3, 2) \).

Calculate the value of \(a + b + 2c\).

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