
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 the graph of a quadratic function $g(x) = dx^2 + ex + f$, where the vertex of the parabola is at $(2, 5)$ and the parabola passes through the point $(3, 2)$. If the distance between grid lines is $1$ unit, find the value of $d+e+2f$.

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