
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
A park charges 5 yuan per person for admission, and offers a group ticket for 40 yuan, which allows a maximum of 10 people to enter.  
(1) There are three groups of students visiting the park, with 6, 8, and 9 members respectively. How should each group buy tickets to save the most money?  
(2) If the three groups have 16, 17, and 18 members respectively, how should each group buy tickets to save the most money?  
(3) If there are x people visiting the park and a total of y tickets are bought, can you find the pattern for the most economical way to purchase tickets?

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