
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
To implement the school-based curriculum plan of "Five Development and Comprehensive Education," Hongxing Middle School organized its teachers and students to participate in a red-themed experiential learning activity. They rented a total of 10 buses of two models, A and B (at least one of each model), to transport 492 students and 10 teachers to the activity. The passenger capacity and rental fees of the two bus models are shown in the table below:

|            | Model A | Model B |
|------------|---------|---------|
| Passenger Capacity (people/bus) | 40 | 55 |
| Rental Fee (RMB/bus) | 600 | 700 |

$(1)$ Find the maximum number of Model A buses that can be rented.  
$(2)$ What are the possible rental plans? Which plan is the most cost-effective?

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