
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 Simplifier is in a soccer league with three other teams, each of which it plays once. In any of its 3 matches, the probabilities that Club Simplifier will win, lose, or tie are $\frac{1}{2}$, $\frac{1}{4}$, and $\frac{1}{4}$, respectively. The probability that Club Simplifier will finish the season with more wins than losses is given by $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.

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