
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
Randomly select two different numbers from $1$, $2$, and $3$, denoted as $m$ and $n$. If the coordinates of point $A$ are denoted as $\left(m,n\right)$, determine the probability that point $A$ lies on the hyperbola $y=\frac{6}{x}$.

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