
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 cubic function \( f(x) = (x-2)(x-1)(x+1) \).

Let \( g(x) = -f(x) \) and \( h(x) = f(-x) \). Determine the value of \( c \) which is the number of points where the graphs of \( y=f(x) \) and \( y=g(x) \) intersect, and \( d \) which is the number of points where the graphs of \( y=f(x) \) and \( y=h(x) \) intersect. Calculate \( 10c + d \).

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