
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
A middle school plans to organize a field trip for some classes. There are 16 teachers and 284 students participating. The school can choose between two types of buses: Bus A, which can hold 30 people and costs 300 yuan, and Bus B, which can hold 42 people and costs 400 yuan. The school plans to keep the total rental cost within 3100 yuan. For safety reasons, each bus must have at least 2 teachers. How many different rental plans are possible, and what is the minimum rental cost?

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