
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 box, there are 10 ping-pong balls of the same size but different colors, including 5 red balls, 3 white balls, and 2 blue balls. Now, a ball is randomly drawn from the box each time. If a blue ball is drawn, the process ends. If a ball that is not blue is drawn, it is put back into the box, and another ball is drawn from the box. However, the number of draws does not exceed 3 times. Find:  
(1) The probability of the process ending after two draws;  
(2) The probability of exactly drawing 2 white balls.

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