
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
During the Spring Festival, electronic firecrackers have become popular due to their safety and lack of pollution. A certain store sells a type of electronic firecracker. It is known that the cost price of this electronic firecracker is $80 per box. Market research has found that the daily sales quantity $y$ (in boxes) of this type of electronic firecracker is related to the selling price $x$ (in dollars) as follows: $y=-2x+320$ ($80\leqslant x\leqslant 160$). Let the daily profit from selling this type of electronic firecracker be $w$ dollars.
1. Find the functional relationship between $w$ and $x$.
2. At what selling price should this type of electronic firecracker be set to maximize the daily profit? What is the maximum profit?
3. If this store wants to make a daily profit of $2400 dollars from selling this type of electronic firecracker and also wants to sell it quickly, what should be the selling price?

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