
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 store sells teapots at \$20 each and teacups at \$5 each. The store offers two promotional discount methods:
(1) Buy 1 teapot and get 1 teacup for free; (2) Pay with a 9.2% discount on the total price.
A customer needs to buy 4 teapots and 4 or more teacups. If the number of teacups purchased is denoted by $x$ (and $x\geq4$), and the amount of money paid is denoted by $y$ (in yuan), establish the function relationship between $y$ and $x$ under each promotional method and discuss which method saves the customer more money when buying the same number of teacups.

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