
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 number of beans are randomly thrown into a square. Upon counting, it is found that a total of 1000 beans fell inside the square, with 780 of them landing within the inscribed circle of the square. Estimate the value of the circumference ratio π (represented as a fraction) as $\boxed{\text{answer}}$.

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