
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
Roll a die twice (the six faces of the die are numbered $1$, $2$, $3$, $4$, $5$, $6$) and let the numbers obtained be $a$ and $b$, respectively. Then, the probability that the line $3x-4y=0$ is tangent to the circle $(x-a)^{2}+(y-b)^{2}=4$ is \_\_\_\_\_\_.

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