
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
Mr. N, aiming to maximize his profit, holds a patent for a unique product and can sell it only in countries A and B. The demand for his product in these countries is represented by the functions \( q_{A}=40-2P \) and \( q_{B}=26-P \), where \( q_{A} \) and \( q_{B} \) are the quantities of the product in countries A and B, respectively, and \( P \) is its price. Resales of Mr. N's product between the countries involve significant costs for his buyers, so Mr. N can set different prices for his product in each country. Regardless of the production country, the shipping cost to the other country is fixed at 1. Mr. N discovered that the production costs of his product do not depend on the production country and are described by the function \( TC(Q)=8Q+1 \). Mr. N can register his enterprise and produce the product in any of the countries, but they have different taxation systems. In country A, there is a proportional tax system with a fixed rate of 15%. In country B, there is a progressive multi-tier taxation system, with the rates indicated in the table:

| Profit | Up to 30 | From 30 to 100 | From 100 to 150 | Above 150 |
| :--- | :--- | :--- | :--- | :--- |
| Tax, % | Exempt | 10 | 20 | 30 |

What will Mr. N's profit be after taxes? What quantity of the product and at what price will be sold in each country?

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