
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 stores, A and B, sell the same item for $200$ yuan each, and there are discounts for buying more items. The discount condition at store A is: the first item is charged at the original price, and each subsequent item is discounted by $30\%$. The discount condition at store B is: each item is discounted by $25\%$. If a customer buys $x$ items, the total cost at store A is $y_{1}$ yuan, and the total cost at store B is $y_{2}$ yuan. <br/>$(1)$ Write the relationship between $y_{1}$, $y_{2}$, and $x$ separately. <br/>$(2)$ Which store is more cost-effective to purchase the item from? Please explain the reason.

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