
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
Xiao Ming and his classmates went to the bookstore to buy books together. They first spent $15$ yuan on a popular science book, and then spent $15$ yuan on a literature book. The price of the popular science book is half higher than the literature book, so they bought one less popular science book than literature book.<br/>$(1)$ What are the prices of the popular science book and the literature book?<br/>$(2)$ If they plan to spend $60$ yuan to buy a total of $10$ books of popular science and literature, how many literature books should they buy at least?

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