
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
The production of \( x \) thousand units of products costs \( q = 0.5x^2 - 2x - 10 \) million rubles per year. With a price of \( p \) thousand rubles per unit, the annual profit from selling these products (in million rubles) is \( p x - q \). The factory produces such a quantity of products that the profit is maximized. What is the minimum value of \( p \) for the total profit over three years to be at least 126 million rubles?

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