
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 that the equation $x^2 + px + q = 0$ has two distinct real roots, denoted as $\alpha$ and $\beta$. Let the set $A = \{\alpha, \beta\}$, $B = \{2, 4, 5, 6\}$, and $C = \{1, 2, 3, 4\}$. Given that $A \cap C = A$ and $A \cap B = \emptyset$, find the values of $p$ and $q$.

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