
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
A bag contains 3 red balls, 2 black balls, and 1 white ball. All 6 balls are identical in every aspect except for color and are well mixed. Balls are randomly drawn from the bag.
(1) With replacement, find the probability of drawing exactly 1 red ball in 2 consecutive draws;
(2) Without replacement, find the probability of drawing exactly 1 red ball in 2 consecutive draws.

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