
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 middle school opened a farming garden to let students experience agricultural labor. They need to purchase a batch of vegetable seedlings to carry out planting activities. It is known that the price of each bundle of type $A$ vegetable seedlings in the market is $1.5$ times that of the vegetable seedling base. With $300$ yuan, $5$ bundles of type $A$ vegetable seedlings were purchased less in 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. The school decided to purchase a total of $100$ bundles of type $A$ and type $B$ vegetable seedlings at the vegetable seedling base, spending no more than $2400. Find the minimum number of bundles of type $A$ vegetable seedlings to be purchased at the vegetable seedling base.

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