
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
Given that the community plans to invest $500$ yuan to purchase three types of books, with type $A$ costing $30$ yuan per book, type $B$ costing $25$ yuan per book, and type $C$ costing $20$ yuan per book, determine the number of purchasing schemes for this procurement plan, where the community must buy at least $5$ books of type $A$ and at most $6$ books of type $A$.

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