
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 fair six-sided die with faces numbered 1, 2, 3, 4, 5, and 6 is rolled twice. Let $a$ and $b$ denote the outcomes of the first and second rolls, respectively.

(1) Find the probability that the line $ax + by + 5 = 0$ is tangent to the circle $x^2 + y^2 = 1$.

(2) Find the probability that the segments with lengths $a$, $b$, and $5$ form an isosceles triangle.

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