
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
A computer generates $2n$ uniform random numbers between $0$ and $1$, denoted as $x_{1}$, $x_{2}$, …$x_{n}$, $y_{1}$, $y_{2}$, …$y_{n}$, forming $n$ pairs of numbers $(x_{1},y_{1})$, $(x_{2},y_{2})$, …$(x_{n},y_{n})$. Among these, there are $m$ pairs of numbers that can form an obtuse triangle with $1$ as one of the sides. The approximate value of $\pi$ obtained by the method of random simulation is \_\_\_\_\_.

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