
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 quadratic function $f(x)=2(x-2)(x+3)$. Define two new functions: $g(x) = -f(x)$, which reflects $f(x)$ about the x-axis, and $h(x) = f(-x)$, which reflects $f(x)$ about the y-axis.

Given that $a$ is the number of intersection points between the graphs of $y = f(x)$ and $y = g(x)$, and $b$ is the number of intersection points between the graphs of $y = f(x)$ and $y = h(x)$, find the value of $10a + b$.

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