
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
A certain distributor plans to purchase two types of agricultural products, $A$ and $B$. It is known that purchasing 2 units of type $A$ and 3 units of type $B$ costs a total of $690$ yuan; purchasing 1 unit of type $A$ and 4 units of type $B$ costs a total of $720$ yuan.  
$(1)$ What is the price per unit of type $A$ and type $B$ respectively?  
$(2)$ If the distributor plans to spend no more than $5400$ yuan to purchase a total of $40$ units of type $A$ and type $B, and the number of units of type $A$ does not exceed 3 times the number of units of type $B$, what is the range of the number of units of type $A$ to be purchased?

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