
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 the 7th grade of the school, a math problem-solving competition is held, and it is planned to purchase notebooks as prizes. According to the prize distribution of the competition, a total of 30 notebooks need to be purchased. It is known that the price of type $A$ notebook is $11$ yuan, and the price of type $B$ notebook is $9$ yuan.  
$(Ⅰ)$ If the school purchases both type $A$ and type $B$ notebooks as prizes, and let $x$ represent the number of type $A$ notebooks purchased.  
① Fill in the table based on the information (express using expressions containing $x$).  

| Type    | Price (yuan/notebook) | Quantity | Cost (yuan) |
|---------|------------------------|----------|-------------|
| $A$     | $11$                   | $x$      | $11x$       |
| $B$     | $9$                    | $30-x$   | $9(30-x)$   |

② If the total cost of purchasing notebooks is $288$ yuan, then how many of type $A$ and type $B$ notebooks should be purchased?  
$(Ⅱ)$ To reduce expenses, the school finally purchases a total of 30 notebooks of type $A$, type $B$, and type $C$ as prizes, where the price of type $C$ notebook is $6$ yuan, and the prices of type $A$ and type $B$ notebooks remain the same. If $m$ type $A$ notebooks and $n$ type $B$ notebooks are purchased.  
① Then the number of type $C$ notebooks purchased is ______, and the total cost of purchasing the three types of notebooks is ______ yuan. (Please express using expressions containing $m$ and $n).  
② If the total cost of purchasing the three types of notebooks is $188$ yuan, then the value of $m$ is ______ (notebooks).

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