
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
From a bag containing 2 red balls and 2 white balls, 2 balls are drawn. Determine which of the following pairs of events are mutually exclusive:  
(1) At least one white ball; both are white balls;  
(2) At least one white ball; at least one red ball;  
(3) Exactly one white ball; exactly two white balls;  
(4) At least one white ball; both are red balls.

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