
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 group of girls live in x dormitories, with 4 people in each dormitory. There are 18 people left without rooms, with 6 people in each dormitory. One dormitory is not full but has students living in it.  
(1) Express the number of girls using an algebraic expression containing x.  
(2) According to the question, write down the system of inequalities involving x, and find the solution set of the inequalities.  
(3) Based on the conclusion in (2), how many dormitories and how many girls could there possibly be in total?

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