
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 is a bag containing 3 red balls and 2 white balls, a total of 5 balls. Draw 2 balls at a time for three times, and place them back after each draw. Calculate:  
(1) The probability that each of the three draws results in one white ball and one red ball;  
(2) The probability that among the three draws, two of them result in one white ball and one red ball, and one draw results in two balls of the same color.

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