
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 factory produces two complementary products, A and B, where producing x tons of product A per day requires the production of x+2 tons of product B. It is known that the cost of producing product A is directly proportional to the square of the output. According to calculations, producing 1 ton of product A requires 40,000 yuan, while the cost of product B is 80,000 yuan per ton.  
(1) Find the minimum average cost of producing products A and B;  
(2) If the supplier's delivery method to this small factory makes the daily production quantity of product A, x, fall within the range of \[0, $\frac{1}{2}$\]∪\[2, 8\], then how many tons of product A should the factory produce each day to minimize the average cost?

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