
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
On a street with a high flow of pedestrians, a middle-aged man is shouting "giving away money". He is holding a black cloth bag, which contains 3 yellow and 3 white ping pong balls (identical in volume and texture). Next to him, there's a small blackboard stating the rules for drawing balls: Draw 3 balls randomly from the bag. If the 3 balls are of the same color, the stall owner will give the drawer 5 yuan; if the 3 balls are of different colors, the drawer pays the stall owner 1 yuan.  
(1) What is the probability of drawing 3 white balls?  
(2) What is the probability of drawing 2 yellow balls and 1 white ball?  
(3) Assuming there are 100 draws per day, estimate how much money the stall owner can make in a month (30 days) from a probability perspective?

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