
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 community needs to purchase two types of garbage bins, $A$ and $B$, in order to carry out the "garbage classification, beautiful Ningbo" activity. With $1600$ yuan, they can buy $14$ bins of type $A$ and $8$ bins of type $B$. It is known that the cost of buying $3$ bins of type $A$ is the same as buying $4$ bins of type $B$. Please answer the following questions:<br/>$(1)$ Find the unit price of bins of type $A$ and type $B$.<br/>$(2)$ If the community wants to purchase a total of $50$ bins of the two types for no more than $3600$ yuan, with at least $29$ bins of type $A$, what are the possible purchasing schemes?

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