
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
Rui Tu welcomes the spring, and the mascot "Tu Yuan Yuan" full of blessings opens the curtain of the 2023 CCTV Spring Festival Gala. The vertical ears, slightly raised head, and upright chest design cleverly show the spirit of progress and upward momentum. A certain store purchased a batch of "Tu Yuan Yuan" toys for 1500 yuan, and after a period of time, purchased another batch of "Tu Yuan Yuan" toys for 3500 yuan. The quantity purchased the second time was twice the quantity purchased the first time, but the price of each "Tu Yuan Yuan" toy was 5 yuan more expensive than the first purchase.  
$(1)$ How many "Tu Yuan Yuan" toys did the store purchase the first time?  
$(2)$ If the store sells the "Tu Yuan Yuan" toys purchased twice at the same selling price, and after selling all of them, the profit is not less than 1150 yuan, then what is the minimum selling price of each "Tu Yuan Yuan" toy?

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