
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 bag contains four balls, each labeled with one of the characters "美", "丽", "惠", "州". Balls are drawn with replacement until both "惠" and "州" are drawn, at which point the drawing stops. Use a random simulation method to estimate the probability that the drawing stops exactly on the third draw. Use a computer to randomly generate integer values between 0 and 3, with 0, 1, 2, and 3 representing "惠", "州", "美", and "丽" respectively. Each group of three random numbers represents the result of three draws. The following 16 groups of random numbers were generated:
232 321 230 023 123 021 132 220
231 130 133 231 331 320 122 233
Estimate the probability that the drawing stops exactly on the third draw.

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