
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
Club Truncator is now in a soccer league with seven other teams, with each match still having a $\frac{1}{3}$ probability of winning, losing, or tying. Club Truncator plays each team once, making a total of 8 matches. Calculate the probability that Club Truncator will finish the season with more wins than losses, in the form $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. What is the sum $m + n$?

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