
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 mascot of the $19^{th}$ Asian Games held in Hangzhou in 2022 is a group of robots named "Jiangnan Yi." The three mascots are named "Cong Cong," "Lian Lian," and "Chen Chen." Among them, "Lian Lian" represents the West Lake, a world heritage site, and its name comes from the endless green lotus leaves in the West Lake. Lotus leaves are loved by people for their purity, nobility, and peaceful appearance. Before the opening day of the Hangzhou Asian Games, a licensed retail store named "Lian Lian" saw increasing sales. According to statistics, the store sold 30,000 items in June 2023 and 36,300 items in August 2023.
  
$(1)$ Find the monthly average growth rate of the sales of the store "Lian Lian."
  
$(2)$ Assuming that the monthly average growth rate of the sales of the store "Lian Lian" remains unchanged, will the sales of "Lian Lian" exceed 40,000 items in September 2023?

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