
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]


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A travel enthusiast plans to choose two countries to visit from three Asian countries \(A_{1}\), \(A_{2}\), \(A_{3}\) and three European countries \(B_{1}\), \(B_{2}\), \(B_{3}\).  
1. If two countries are chosen at random from these six, find the probability that both countries are Asian.  
2. If one country is chosen at random from the Asian countries and one from the European countries, find the probability that these two countries include \(A_{1}\) but do not include \(B_{1}\).

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