
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
In a random number simulation experiment, if $x = 3 \cdot \text{rand()}$ and $y = 2 \cdot \text{rand()}$ (where $\text{rand()}$ represents a random number generated between $0$ and $1$), and after performing $m$ trials, there are $n$ trials that satisfy $\frac{x^2}{9} + \frac{y^2}{4} \leq 1$, then the area of the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ can be estimated as __________.

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