
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
Let \(f(x) = (x-2)(x-5)\), and define \(g(x) = 2f(x)\) and \(h(x) = f(-x) + 2\). Determine the number of points where the graphs of \(y=f(x)\) and \(y=g(x)\) intersect, represented by \(a\), and where \(y=f(x)\) and \(y=h(x)\) intersect, represented by \(b\). Compute \(10a + b\).

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