
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
Teacher Huang plans to start a badminton club on Friday. She plans to buy 16 badminton rackets and $x$ boxes of shuttlecocks $\left(x \gt 16\right)$. Teacher Huang found that two stores, Store A and Store B near the school, are selling the same brand of badminton rackets and shuttlecocks. The price of each badminton racket is $150 yuan, and the price of each box of shuttlecocks is $40 yuan. After negotiating with the teacher, Store A offers a promotion of one box of shuttlecocks for every badminton racket purchased, while Store B offers a discount of 20% off for all badminton rackets and shuttlecocks.<br/>$(1)$ Teacher Huang buys badminton rackets and shuttlecocks, and pays $y_{A}$ and $y_{B}$ yuan at Store A and Store B, respectively.<br/>Write directly: $y_{A}=$______ yuan, $y_{B}=$______ yuan (express using an expression containing $x$):<br/>$(2)$ When $x=25$, which store is more cost-effective for Teacher Huang to buy these badminton rackets and shuttlecocks? Please explain the reason.

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