
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 a quadratic function $f(x) = x^2 - 4x + 3$, let $g(x) = -f(x)$ and $h(x) = f(-x)$. Calculate the number of intersection points between the graph of $y = f(x)$ and $y = g(x)$, and between $y = f(x)$ and $y = h(x)$. Express your final answer as $10a + b$ where $a$ is the number of intersection points between $y = f(x)$ and $y = g(x)$, and $b$ is the number between $y = f(x)$ and $y = h(x)$.

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