
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
Given the quadratic function $f(x) = (x-2)(x-4)$, define $g(x) = -f(x)$ and $h(x) = f(-x)$. If $c$ is the number of points where the graphs of $y = f(x)$ and $y = g(x)$ intersect, and $d$ is the number of points where the graphs of $y = f(x)$ and $y = h(x)$ intersect, determine the value of $10c + d$.

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