
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
In 2023, Zhengzhou launched the "Construction Plan" for landscaping, focusing on creating a green city with blue skies, green land, and clean water, making Zhengzhou a livable, business-friendly, and tourist-friendly city. A certain scenic area plans to renovate a green area by planting two types of flowers, $A$ and $B$. It is known that the cost of planting 3 pots of type $A$ flowers and 4 pots of type $B$ flowers is 360 yuan, and the cost of planting 4 pots of type $A$ flowers and 3 pots of type $B$ flowers is 340 yuan. <br/>$(1)$ What is the cost of planting each pot of type $A$ flowers and each pot of type $B$ flowers? <br/>$(2)$ If the scenic area plans to plant a total of 600 pots of type $A$ and type $B$ flowers this year, with data showing that the survival rates of type $A$ and type $B$ flowers are 70% and 90% respectively, the scenic area plans to replace the dead flowers with the same number of new flowers next year. However, the total number of pots of both types of flowers replaced next year should not exceed 100 pots. How should the planting quantities of these two types of flowers be arranged to minimize the planting cost for this year? And what is the minimum cost?

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