
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 2022, the Ministry of Education issued the "Compulsory Education Curriculum Plan" and the curriculum standard (2022 edition), separating labor from the original comprehensive practical activities course. A certain middle school opened a farming garden to allow students to experience agricultural labor. They need to purchase two types of vegetable seedlings, $A$ and $B$, from a vegetable seedling base to carry out planting activities. If they buy 30 bundles of type $A$ seedlings and 10 bundles of type $B$ seedlings, it will cost a total of 380 yuan; if they buy 50 bundles of type $A$ seedlings and 30 bundles of type $B$ seedlings, it will cost a total of 740 yuan. <br/>$(1)$ Find the unit price per bundle of type $A$ and type $B$ seedlings from the vegetable seedling base; <br/>$(2)$ The school decides to spend 828 yuan to purchase 100 bundles of type $A$ and type $B$ seedlings from the vegetable seedling base. The vegetable seedling base supports the school's activities and offers a 10% discount on both type $A$ and type $B$ seedlings. Find the maximum number of bundles of type $A$ seedlings that can be purchased this time.

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