
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
To create a civilized city and build a beautiful home, the Happy Community decides to purchase two models of new trash cans, $A$ and $B$, to raise awareness of garbage classification. If purchasing 3 $A$ type trash cans and 4 $B$ type trash cans costs a total of $580, and purchasing 6 $A$ type trash cans and 5 $B$ type trash cans costs a total of $860. <br/> $(1)$ Find the unit prices of the two types of trash cans; <br/> $(2)$ If a total of 200 $A$ and $B$ type trash cans are needed, and the total cost does not exceed $15000, how many $A$ type trash cans should be purchased at least?

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