
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's horse racing with the King of Qi is a famous historical tale. Supposing the King of Qi has three horses \\(A\\), \\(B\\), \\(C\\), and Tian Ji has three horses \\(a\\), \\(b\\), \\(c\\); each horse races once, and the one who wins two or more races is the winner. The relative strength of the 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 surely use his top horse \\(A\\) in the first race. Tian Ji then adopts the most appropriate strategy in response—what is the probability of Tian Ji winning using this strategy?

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