
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 a quadratic function $p(x) = x^2 - 4x + 3$, and let $q(x) = -p(x) + 2$ and $r(x) = p(-x)$. Compute the number of intersection points between the graphs of $y = p(x)$ and $y = q(x)$, denoted as $c$. Also, compute the number of intersection points between the graphs of $y = p(x)$ and $y = r(x)$, denoted as $d$. Calculate the value of $10c + d$.

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