
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
If $r_1$ and $r_2$ are the distinct real roots of $x^2+px+9=0$, then which of the following statements must be true?
1. $|r_1+r_2| > 4\sqrt{2}$
2. $|r_1| > 3 \; \text{or} \; |r_2| > 3$
3. $|r_1| > 3$
4. $|r_1| < 3 \; \text{and} \; |r_2|<3$
5. $r_1 < 0 \; \text{and} \; r_2 < 0$
A) $|r_1+r_2| > 4\sqrt{2}$
B) $|r_1| > 3 \; \text{or} \; |r_2| > 3$
C) $|r_1| > 3$
D) $|r_1| < 3 \; \text{and} \; |r_2|<3$
E) $r_1 < 0 \; \text{and} \; r_2 < 0$

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