
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
Consider the graph of a quadratic function given by $f(x) = \frac{(x-2)(x-4)}{3} + 1$.

Let $g(x) = -f(x)$ and $h(x) = f(x) - 3$. If $a$ is the number of points where the graphs of $y=f(x)$ and $y=g(x)$ intersect, and $b$ is the number of points where the graphs of $y=f(x)$ and $y=h(x)$ intersect, find the value of $10a + b$.

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