
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
To welcome the air show and beautify Zhuhai, the gardening department decided to use the existing 2660 pots of Type A flowers and 3000 pots of Type B flowers to arrange 50 sets of two types of gardening styles, A and B, along the Zhuhai Avenue. It is known that arranging one set of Style A requires 70 pots of Type A flowers and 30 pots of Type B flowers, while arranging one set of Style B requires 40 pots of Type A flowers and 80 pots of Type B flowers.  
(1) A company has undertaken the design of this gardening style arrangement plan. How many feasible arrangement plans are there according to the problem? Please help to design them.  
(2) If the cost of arranging one set of Style A is 800 yuan, and the cost of arranging one set of Style B is 960 yuan, which of the plans in (1) has the lowest cost? What is the lowest cost?

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