
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
Recently, the Ministry of Education issued the "Compulsory Education Curriculum Plan" and the curriculum standards (2022 edition), separating labor from the original comprehensive practice activities course. A certain middle school opened a farming garden to allow students to experience agricultural labor and needed to purchase a batch of vegetable seedlings for planting activities. It is known that the price of each bundle of type $A$ vegetable seedlings on the market is $5/4$ times that of the vegetable seedling base. With $300$ yuan, the school purchased $3$ fewer bundles of type $A$ vegetable seedlings on the market than at the vegetable seedling base.<br/>$(1)$ Find the price of each bundle of type $A$ vegetable seedlings at the vegetable seedling base.<br/>$(2)$ The price of each bundle of type $B$ vegetable seedlings at the vegetable seedling base is $30$ yuan. The school decided to purchase $100$ bundles of type $A$ and type $B$ vegetable seedlings at the vegetable seedling base, with the number of bundles of type $A$ vegetable seedlings not exceeding the number of bundles of type $B$ vegetable seedlings. The vegetable seedling base offered a 10% discount on both type $A$ and type $B$ vegetable seedlings to support the school's activities. Find the minimum amount spent on this purchase.

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