
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
Three numbers (x, y, z) are randomly selected from the interval [0,1]. If they satisfy x^2 + y^2 + z^2 > 1, then the parameter t = 1; otherwise, t = 0. Based on this, the sum of all parameters from 1000 repeated experiments is 477, determine the estimated value of the constant π.

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