
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 certain garden charges $10$ yuan for each ticket, which can be used only once. In consideration of different needs of people and to attract more visitors, the garden has introduced a new ticketing method of "buying a personal annual pass" (the annual pass can be used by the holder for one year from the date of purchase). The annual passes are divided into three categories: $A$, $B$, and $C. The $A$ pass costs $120$ yuan per pass, and the holder can enter the garden without buying a ticket again; the $B$ pass costs $60$ yuan per pass, and the holder needs to buy a ticket again for $2$ yuan each time entering the garden; the $C$ pass costs $40$ yuan per pass, and the holder needs to buy a ticket again for $3$ yuan each time entering the garden.

(1) If you choose only one way to buy tickets and plan to spend $80$ yuan on tickets in the garden within a year, try to calculate and find the ticketing method that allows you to enter the garden the most times.

(2) Find out how many times you need to enter the garden in a year for buying the $A$ pass to be more cost-effective.

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