
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
King Qi and Tian Ji have a horse race, each with three horses. Tian Ji's best horse is better than King Qi's average horse but worse than King Qi's best horse. Tian Ji's average horse is better than King Qi's worst horse but worse than King Qi's average horse. Tian Ji's worst horse is worse than King Qi's worst horse. They compete in three races, each time sending out one horse that has not competed before. The one who wins more races is considered the victor. What is the probability of Tian Ji winning?

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