
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
In a class of 25 students, each student is either a good student or a troublemaker. Good students always tell the truth, while troublemakers always lie.

One day, 5 students from this class said: "If I transfer to another class, more than half of the remaining students will be troublemakers."

Each of the remaining 20 students said: "If I transfer to another class, the number of troublemakers among the remaining students will be three times the number of good students."

How many good students are in the class? List all possible options.

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