
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
In a bag, there are one red ball and one white ball. A ball is drawn at random with replacement three times. Calculate the probabilities of the following events:  
(1) Exactly two of the three colors drawn are the same;  
(2) All three colors drawn are the same;  
(3) The number of times a red ball is drawn is more than the number of times a white ball is drawn.

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