
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
An art exhibition was held at a certain exhibition center on Saturday and Sunday. The total number of visitors on Saturday was 300. The number of visitors on Sunday morning increased by 40% compared to Saturday morning, and the number of visitors on Sunday afternoon increased by 30% compared to Saturday afternoon. The total number of visitors on Sunday was 100 more than on Saturday. (Visitors include adults and middle school students)<br/>$(1)$ Find the number of visitors on Sunday morning and afternoon.<br/>$(2)$ It is known that the tickets for the art exhibition are divided into adult tickets and middle school student tickets. The total ticket revenue on Sunday morning was $4200, and the total ticket revenue in the afternoon was $7200. There were 70 adults visiting in the morning and 100 adults visiting in the afternoon on Sunday.<br/>① Find the price of each adult ticket and middle school student ticket.<br/>② Jiajia said, "The total ticket revenue on Saturday cannot be $8390." Please explain the reason.

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