
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]


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To enhance students' physical fitness, our school has set up sports interest classes for seventh graders. Among them, the basketball interest class has $x$ students, the number of students in the soccer interest class is $2$ less than twice the number of students in the basketball interest class, and the number of students in the volleyball interest class is $2$ more than half the number of students in the soccer interest class.  
$(1)$ Express the number of students in the soccer interest class and the volleyball interest class with algebraic expressions containing variables.  
$(2)$ Given that $y=6$ and there are $34$ students in the soccer interest class, find out how many students are in the basketball interest class and the volleyball interest class.

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