
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
$(1)$ Reading material: We know that $4x+2x-x=(4+2-1)x=5x$. Similarly, if we consider $(a+b)$ as a whole, then $4(a+b)+2(a+b)-(a+b)-(4+2-1)(a+b)=5(a+b)$. The "whole idea" is an important thinking method in solving problems in secondary school teaching, and it is widely used in the simplification and evaluation of polynomials. Try to apply: ① Consider $(a+b)$ as a whole, merge $-3(a+b)^2-6(a+b)^2+8(a+b)^2$ to get ______. ② Broaden exploration: Given $a-2b=5$, $2b-c=-7$, $c-d=12$, find the value of $4(a-c)+4(2b-d)-4(2b-c)$.<br/>$(2)$ A person bought 8 sets of electronic products for 400 yuan, preparing to sell them at a certain price. If each set of electronic products is sold at a standard price of 56 yuan, with the excess recorded as a positive number and the shortfall as a negative number, the records are as follows (unit: yuan): $-3$, $+7$, $-8$, $+9$, $-2$, $0$, $-1$, $-6$. After selling these 8 sets of electronic products, will he make a profit or a loss?

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