
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 response to the call for bringing traditional culture into schools, a certain school decided to purchase the books "Analects" and "Standards for Being a Good Student and Child" from an online store for students' extracurricular reading. The purchasing information for the two books is as follows:

| "Analects" Quantity / books | "Standards for Being a Good Student and Child" Quantity / books | Total Cost (yuan) |
|-----------------------------|---------------------------------------------------------------|-------------------|
| 40                          | 30                                                            | 1250              |
| 50                          | 20                                                            | 1300              |

$(1)$ What is the price per book for "Analects" and "Standards for Being a Good Student and Child" respectively?

$(2)$ If the school plans to purchase a total of 100 books of "Analects" and "Standards for Being a Good Student and Child," with the quantity of "Standards for Being a Good Student and Child" not exceeding twice the quantity of "Analects," please design the most cost-effective purchasing plan and calculate the total cost of this plan.

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