
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 that $2n$ numbers $x_{1}$, $x_{2}$, ..., $x_{n}$, $y_{1}$, $y_{2}$, ..., $y_{n}$ are randomly selected from the interval $[0,1]$ and paired, calculate the approximate value of the circumference ratio $\pi$ obtained by the method of random simulation.

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