
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 in succession.
(1) List or draw a tree diagram to show all possible outcomes of the numbers on the faces that come up.
(2) Let the numbers on the faces that come up in the two rolls be $m$ and $n$, respectively. If $m$ and $n$ are used as the coordinates of point $P(m, n)$, calculate the probability that point $P(m, n)$ lies on the hyperbola $y = \frac{1}{x}$.

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