
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
In 2023, Guizhou Province introduced the "Attracting Tourists to Guizhou" team tourism and marketing incentive measures to boost the strong recovery of the tourism market. A travel agency rented two types of rooms, $A$ and $B$, in a certain scenic area on May 1st for one day with the following information: the number of rooms rented for $6000$ yuan for room $A$ is equal to the number of rooms rented for $4400$ yuan for room $B$. It is known that the unit price of each room in type $A$ is $80$ yuan more than the unit price of each room in type $B$. <br/>$(1)$ Find the unit prices of rooms $A$ and $B$ respectively;<br/>$(2)$ If a total of $30$ rooms of types $A$ and $B$ are rented, the number of rooms of type $A$ is not less than half the number of rooms of type $B$, and the total cost does not exceed $7600$ yuan, find all possible rental schemes.

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