
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
There are 27 students in the class, but not all of them came to the physical education lesson. The teacher divided those who came into two equal teams for a game of dodgeball. In the first team, there were half of all the boys who came and a third of all the girls who came, and in the second team, there were half of all the girls who came and a quarter of all the boys who came. The remaining students helped as referees. How many assistants could the referee have had?

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