
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), which separated labor from the original comprehensive practical activities course and released the "Compulsory Education Labor Course Standard (2022 edition)." Through labor education, students can not only cultivate survival skills but also exercise their willpower, guide students to establish a sense of labor, cultivate the most basic labor habits, and ultimately form a correct new era labor values. A certain middle school in Erqi District, Zhengzhou City opened a farming garden for students to experience farming 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 $15$ bundles of type $A$ seedlings and $5$ bundles of type $B$ seedlings, it will cost a total of $190$ yuan; if they buy $25$ bundles of type $A$ seedlings and $15$ bundles of type $B$ seedlings, it will cost a total of $370$ yuan.
$(1)$ Find the unit price per bundle of type $A$ and type $B$ seedlings from the vegetable seedling base;
$(2)$ 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}
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