
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
The story of Tian Ji and the King of Qi racing horses is a famous historical tale. Suppose the King of Qi's three horses are respectively named A, B, C, and Tian Ji's three horses are named a, b, c. Each horse races once, and the one who wins two out of three races is the victor. If the relative strengths of these six horses can be represented by the following inequalities: A > a > B > b > C > c  
(1) Under normal circumstances, calculate the probability of Tian Ji winning.  
(2) To increase his chances of winning, Tian Ji sends a scout to gather intelligence on the King of Qi and learns that the King will definitely use his top horse, A, in the first race. Tian Ji then adopts the most appropriate strategy. Calculate the probability of Tian Ji winning under this scenario.

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