
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 the curves $y = 2x^2 + px + q$ and $y = -x^2 + rx + s$, where $p, q, r,$ and $s$ are integers, and $p, r \in \{1, 2, 3\}$, $q, s \in \{0, 1\}$, find the probability that the curves have at least one point in common.

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