
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
Aunt Wang, a laid-off worker, utilized her expertise to start the "Loving Heart Clothing Factory," planning to produce a total of 40 sets of two types of clothing, Type A and Type B, for market sales. It is known that the cost per set of Type A clothing is 34 yuan, with a selling price of 39 yuan; the cost per set of Type B clothing is 42 yuan, with a selling price of 50 yuan. The factory expects the cost of the two types of clothing to be no less than 1536 yuan and no more than 1552 yuan.
(1) What are the production plans for the factory?
(2) According to the production plans in (1), what is the minimum profit that can be obtained if all the clothing is sold?

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