
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
Calligraphy is a cultural treasure of the Chinese nation, a precious wealth of human civilization, and an important part of basic education in our country. A certain school is preparing to purchase a batch of brushes and rice paper for students' calligraphy classes. It is known that purchasing 40 brushes and 100 sheets of rice paper costs 280 yuan; purchasing 30 brushes and 200 sheets of rice paper costs 260 yuan.  
$(1)$ Find the unit prices of the brushes and rice paper.  
$(2)$ If the school plans to purchase a total of 200 brushes and rice paper with no more than 360 yuan, how many brushes can the school purchase at most?

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