
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
The total number of football teams from the East and West participating in the Super League does not exceed 30 teams. The East has 1 more team than the West. Every pair of teams played a match against each other: a win earns 3 points, a draw earns 1 point, and a loss earns 0 points. After the league ended, the results showed that the ratio of wins to draws among teams within the East, within the West, and between the East and West is 2:1. However, the total points of all teams in the East is 34 points more than the total points of all teams in the West. How many teams from the East and how many teams from the West participated in the competition?

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