
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
A dice is thrown twice. Let $a$ be the number of dots that appear on the first throw and $b$ be the number of dots that appear on the second throw. Given the system of equations $\begin{cases} ax+by=2 \\\\ 2x+y=3\\end{cases}$.

(I) Find the probability that the system of equations has only one solution.

(II) If each solution of the system of equations corresponds to a point $P(x,y)$ in the Cartesian plane, find the probability that point $P$ lies in the fourth quadrant.

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