
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]


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(The full score for this question is 12 points) Zhengding Middle School organizes students from the east and west schools to use their Sunday time to participate in a charity activity at Hope Primary School, with at least one student from each school participating. It is known that the round-trip bus fare for each student from the east school is 3 yuan, and each can serve 5 primary school students; the round-trip bus fare for each student from the west school is 5 yuan, and each can serve 3 primary school students. If it is required that the number of students participating from the west school is at least one more than that from the east school, and the total round-trip bus fare for students from both schools to Hope Primary School does not exceed 37 yuan, how should the number of students participating from the east and west schools be arranged to maximize the number of primary school students served? What is the maximum number of primary school students that can be served?

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