
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
Huqiu Agricultural Machinery School plans to send 6 class teachers and 234 students from the seventh grade to Hefei for a visit and study. The principal is considering using either 45-seat large buses or 30-seat small buses. If renting 1 large bus and 2 small buses costs a total of 1000 yuan, and renting 2 large buses and 1 small bus costs a total of 1100 yuan.  
(1) What is the rental cost per bus for both large and small buses?  
(2) For safety, the principal requires that there be at least one teacher on each bus, and the total rental cost must not exceed 2300 yuan. Can you come up with the most cost-effective rental plan? Please write it down.

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