
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
Xinyi is a beautiful city with abundant tourism resources. The Malingshan Scenic Area is a $4A$-rated tourist attraction in our city. The scenic area has developed a souvenir that costs $30$ yuan to produce and is sold. The selling price is set not to be lower than the cost and not higher than $54$ yuan. After selling for a period of time, it was found that when the product was priced at $40$ yuan, 80 units could be sold per day. Furthermore, for every $1$ yuan increase in the selling price, the daily sales volume would decrease by 2 units. If the goal is to make a profit of $1200$ yuan per day from selling this product, please determine the selling price at that time.

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