
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 for $25$ yuan each and tea cups for $5 yuan each. The store has two discount schemes: Scheme 1: Buy one teapot and get one tea cup for free; Scheme 2: Pay $94\%$ of the total price. A customer needs to buy 4 teapots and $x$ tea cups $\left(x\geqslant 4\right)$. <br/>$(1)$ Calculate how much money the customer needs to pay for each of the two discount schemes. <br/>$(2)$ When $x=47$, which scheme is more cost-effective?

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