
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
Two tour groups, Group A and Group B, are traveling to Suzhou at the same time. It is known that Group B has 4 more people than Group A. The sum of the number of people in the two groups is exactly 18 times the difference between the number of people in the two groups.  
$(1)$ What are the numbers of people in Group A and Group B, respectively?  
$(2)$ If the number of children in Group B is 2 less than three times the number of children in Group A, and the adult ticket price at a certain scenic spot is $100$ yuan per ticket, with children's tickets being 40% off the adult price, and the two tour groups spend the same amount on tickets at this scenic spot, what are the numbers of children in Group A and Group B, respectively?

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