
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
During the epidemic prevention and control period, people should wear masks when going out to protect themselves from being infected with the novel coronavirus. A certain pharmacy purchased a certain number of packs of disposable medical masks for $4000$ yuan, which were quickly sold out. The store then purchased a second batch of the same masks for $7500$ yuan. The number of packs purchased in the second batch was $50\%$ more than the first batch, and the cost per pack of masks in the second batch was $0.5$ yuan more than the cost per pack in the first batch. Please answer the following questions:<br/>$(1)$ How many packs of medical masks were purchased in the first batch?<br/>$(2)$ The government took measures to keep the selling price consistent for these two batches of medical masks. If the total profit from selling these two batches of masks does not exceed $3500$ yuan, what is the highest selling price per pack that the pharmacy can set?

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