
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
There are four balls in a bag, each labeled with one of the four characters "中" (Zhong), "华" (Hua), "民" (Min), "族" (Zu). A ball is randomly drawn from the bag with replacement until both "中" and "华" are drawn. Estimate the probability of stopping after exactly three draws using a random simulation. Generate random integers between 0 and 3 using a computer, where 0, 1, 2, 3 represent "中", "华", "民", "族" respectively. Group the results into sets of three to represent the outcomes of three draws. After conducting a random simulation, the following 18 sets of random numbers were generated: <br/>$232$  $321$  $230$  $023$  $123$  $021$  $132$  $220$  $001$ <br/>$231$  $130$  $133$  $231$  $031$  $320$  $122$  $103$  $233$ <br/>Based on this, estimate the probability of stopping after exactly three draws to be ______.

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