
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
Given the interval $[0,1]$, randomly extract $2n$ numbers $x_1$, $x_2$, ..., $x_n$, $y_1$, $y_2$, ..., $y_n$, forming $n$ pairs of numbers $(x_1,y_1)$, $(x_2,y_2)$, ..., $(x_n, y_n)$. Among these pairs, there are $m$ pairs whose sum of squares is less than $1$, find the approximate value of the circumference ratio $\pi$.

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