
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
168 players participated in an encryption game in 50 teams, with each team having two to five members. The most common team size was four members, there were 20 teams with three members, and there was at least one team with five members. How many teams had two members, four members, and five members?

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