
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
The equation of curve $C$ is $\frac{x^2}{m^2} + \frac{y^2}{n^2} = 1$, where $m$ and $n$ are the numbers obtained by rolling a die twice in succession. Let event $A$ be "The equation $\frac{x^2}{m^2} + \frac{y^2}{n^2} = 1$ represents an ellipse with foci on the $x$-axis". Then, the probability of event $A$ occurring, $P(A)=$ .

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