
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 Dynamo is in a football league with nine other teams, each of which it plays twice. In any of its 18 matches, the probabilities that Club Dynamo will win, lose, or tie are 0.4, 0.4, and 0.2, respectively. Find the probability that Club Dynamo will finish the season with more wins than losses, and express this as a fraction $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

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