
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
Throw a dice twice, observe the numbers that appear, and let the number that appears first be $a$, and the number that appears second be $b$.

$(1)$ The probability that the sum of the numbers is greater than $7$.

$(2)$ Given the system of equations $\begin{cases} & ax+by=3 \\ & x+2y=2 \\ \end{cases}$, find the probability that the system has only one solution.

$(3)$ Given the system of equations $\begin{cases} & ax+by=3 \\ & x+2y=2 \\ \end{cases}$, find the probability that the system has only positive solutions.

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