
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
At the "Economics and Law" congress, a "Best of the Best" tournament was held, in which more than 220 but fewer than 254 delegates—economists and lawyers—participated. During one match, participants had to ask each other questions within a limited time and record correct answers. Each participant played with each other participant exactly once. A match winner got one point, the loser got none, and in case of a draw, both participants received half a point each. By the end of the tournament, it turned out that in matches against economists, each participant gained half of all their points. How many lawyers participated in the tournament? Provide the smallest possible number as the answer.

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