
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 sets $A=\{-1, 0, 1\}$ and $B=\{-2, -1, 0, 1, 2\}$, now select one number from each of the sets $A$ and $B$.
(1) Find the probability that the sum of these two numbers is 0;
(2) If the numbers selected from sets $A$ and $B$ are denoted as $a$ and $b$ respectively, find the probability that the system of equations $$\begin{cases} ax+by=3 \\ x+2y=2 \end{cases}$$ has only one solution.

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