
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
The 19th Asian Games will be held in Hangzhou from September 23 to October 8, 2023. A certain store purchased ornaments and pendants of the Asian Games mascot for 25,000 yuan and made a total profit of 11,700 yuan after selling them. The ornaments were purchased at 40 yuan each and sold at 58 yuan each, while the pendants were purchased at 30 yuan each and sold at 45 yuan each. <br/> $(1)$ Please find the quantities of ornaments and pendants purchased by the store. (Solve the problem using a system of two linear equations) <br/> $(2)$ During the 618 promotion period, the store purchased ornaments and pendants at the original purchase price for the second time. The quantity of ornaments purchased remained the same, while the quantity of pendants purchased was twice that of the first time. The ornaments were sold at the original selling price, while the pendants were sold at a discounted price. If the store wants to make a profit of at least 10,800 yuan from the second round of operations after selling all the items, what is the minimum discount percentage that can be applied to the pendants? (Solve the problem using a linear inequality)

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