
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
On the eve of the new school year, a bookstore plans to purchase a total of 350 notebooks of two types, $A$ and $B$. It is known that the cost price of type $A$ notebooks is $12$ yuan per notebook, and the cost price of type $B$ notebooks is $15$ yuan per notebook, totaling $4800$ yuan.<br/>$(1)$ How many notebooks of type $A$ were purchased?<br/>$(2)$ During the sales process, the selling prices of type $A$ and type $B$ notebooks are $20$ yuan per notebook and $25$ yuan per notebook, respectively. Due to the impact of the epidemic, after selling $m$ notebooks of each type at the selling price, the store conducted a promotion. The remaining type $A$ notebooks were sold at 30% off the selling price, and the remaining type $B$ notebooks were cleared at cost price. If the total profit from the two types of notebooks is not less than $2348$ yuan, find the minimum value of $m$.

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