
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 \( g(x) = -f(x) \) and \( h(x) = f(-x) \). Determine the number of points where the graphs of \( y=f(x) \) and \( y=g(x) \) intersect, denoted as \( a \), and the number of points where the graphs of \( y=f(x) \) and \( y=h(x) \) intersect, denoted as \( b \). What is \( 10a+b \)?

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