
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 celebrate the New Year's Day event, a certain middle school organized a large chorus competition. Class A and Class B together have a total of 92 people (with Class A having more than 51 people but less than 55 people) preparing to purchase uniforms for the performance. Below is a price list of performance costumes provided by a clothing factory:<br/>

| Number of Sets | 1 set to 50 sets | 51 sets to 90 sets | 91 sets and above |
|-----------------|-------------------|--------------------|-------------------|
| Price per set   | $50              | $40                | $30               |

$(1)$ The total amount to be paid for Class A and Class B together to purchase uniforms is ______ yuan;<br/>
$(2)$ If the two classes separately purchase uniforms and the total amount paid is $4080$ yuan, how many students from Class A and Class B are preparing to participate in the performance?<br/>
$(3)$ If 8 students from Class A are selected to participate in a calligraphy and painting competition and cannot participate in the performance, please design the most cost-effective uniform purchase plan for the two classes.

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