
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 period of "fighting the epidemic", the school union of a certain school called on teachers to actively carry out the "donation of love" activity. The school plans to use this donation to purchase two types of epidemic prevention supplies, $A$ and $B$. If $60$ units of type $A$ items and $45$ units of type $B$ items are purchased, the total cost is $1140$ yuan; if $45$ units of type $A$ items and $30$ units of type $B$ items are purchased, the total cost is $840$ yuan.  
$(1)$ Find the price of each unit of type $A$ and type $B$ epidemic prevention supplies.  
$(2)$ Now, it is required to purchase a total of $600$ units of type $A$ and type $B$ epidemic prevention supplies, with a total cost not exceeding $8000$ yuan. How many units of type $A$ epidemic prevention supplies can be purchased at most?

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