
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 are having a horse race. Tian Ji's top horse is better than King Qi's middle horse but worse than King Qi's top horse. Tian Ji's middle horse is better than King Qi's lower horse but worse than King Qi's middle horse. Tian Ji's lower horse is worse than King Qi's lower horse. Determine the probability that Tian Ji wins if one horse is randomly selected from both sides for a race.

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