
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
A study group consists of students and teachers, and the composition of the group meets the following three conditions:

(1) The number of male students is greater than the number of female students;  
(2) The number of female students is greater than the number of teachers;  
(3) The number of teachers doubled is more than the number of male students.  
① If the number of teachers is $4$, then the maximum number of female students is $\boxed{6}$.  

② The minimum number of people in the group is $\boxed{12}$.

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