
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 24th Winter Olympics concluded in Beijing on February 20, 2022, and the mascots Bing Dwen Dwen and Shuey Rhon Rhon are selling well in the market. A certain franchise store is preparing to purchase a certain number of Bing Dwen Dwen and Shuey Rhon Rhon mascots, with their purchase prices and selling prices as shown in the table below:

|              | Bing Dwen Dwen Mascot | Shuey Rhon Rhon Mascot |
|--------------|-----------------------|------------------------|
| Purchase Price (元/each) | $m$                   | $m-30$                 |
| Selling Price (元/each)  | $190$                 | $140$                  |

It is known that the quantity of Bing Dwen Dwen mascots purchased for $3000$ yuan is the same as the quantity of Shuey Rhon Rhon mascots purchased for $2400$ yuan.

$(1)$ Find the value of $m$;  
$(2)$ If you want to purchase a total of $200$ mascots of the two kinds, and in order to promote the upcoming Winter Paralympic Games, the quantity of Shuey Rhon Rhon mascots purchased must not be less than $\frac{2}{3}$ of the quantity of Bing Dwen Dwen mascots. How should you purchase the goods to maximize profit?

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