
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 \( f(x) = (x + 2)(x - 4) \).
Define transformations \( g(x) = -f(x) \) and \( h(x) = f(2x) \). Find the number of points where the graphs of \( y = f(x) \) and \( y = g(x) \) intersect, called \( a \), and the number of points where \( y = f(x) \) and \( y = h(x) \) intersect, called \( b \). Calculate \( 10a + b \).

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