
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
A newly created "Countryside Scenery" scenic area in a certain township plans to renovate a green area and plant two types of flowers, $A$ and $B$. It is known that the planting cost for 3 pots of type $A$ flowers and 4 pots of type $B$ flowers is 330 yuan, and the planting cost for 4 pots of type $A$ flowers and 3 pots of type $B$ flowers is 300 yuan.  
$(1)$ What is the cost per pot for type $A$ flowers and type $B$ flowers, respectively?  
$(2)$ If the scenic area plans to plant a total of 400 pots of type $A$ and type $B$ flowers this year, with data indicating 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 new flowers next year. However, the total number of pots of both types of flowers replaced next year should not exceed 80 pots. How should the planting quantities of these two types of flowers be arranged to minimize the planting cost for this year? What is the minimum cost?

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