
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 school organized its eighth-grade students to participate in a social practice activity. If they rent several 35-seat buses, they can exactly fill them up. However, if they rent 55-seat buses instead, they can rent one less bus and still have 45 empty seats left.  
(1) Find the number of eighth-grade students participating in the social practice activity.  
(2) Given that the rental cost for a 35-seat bus is 320 yuan per bus, and for a 55-seat bus is 400 yuan per bus. Based on a budget that the rental cost should not exceed 1500 yuan, the school decides to rent a total of 4 buses of these two types (which can be underfilled). Calculate the rental cost for the vehicles needed for this social practice activity.

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