
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
With the successful hosting of the 24th Beijing Winter Olympics and Paralympics, "Bing Dwen Dwen" and "Shuey Rong Rong" have become mascots that everyone is eager to get. Seizing this business opportunity, a certain merchant quickly purchased a batch of "Bing Dwen Dwen" and "Shuey Rong Rong" small pendants. It is known that 2 "Bing Dwen Dwen" and 1 "Shuey Rong Rong" pendant cost a total of 26 yuan, and 4 "Bing Dwen Dwen" and 3 "Shuey Rong Rong" pendants cost a total of 62 yuan.<br/>$(1)$ What is the price of each "Bing Dwen Dwen" and "Shuey Rong Rong" pendant?<br/>$(2)$ If this merchant is preparing to purchase another 100 "Bing Dwen Dwen" and "Shuey Rong Rong" pendants, with the quantity of "Shuey Rong Rong" not less than $\frac{1}{3}$ of the quantity of "Bing Dwen Dwen," please design the most cost-effective purchasing plan and calculate the minimum cost.

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