
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. When it lands, the number of dots facing up is considered the result of that throw, which can randomly be any number from 1 to 6. Throw the dice twice in a row, let the number of dots for the first throw be $a$, and for the second throw be $b$.
(1) Find the probability that the line $ax+by=0$ is parallel to the line $x+2y+1=0$;
(2) Find the probability that three line segments with lengths $a$, $b$, and $2$ can form a triangle.

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