
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 supply of a certain good in a competitive market can be described by the function $Q^{S}(p) = 2 + 8p$ (where $Q$ is the quantity sold, and $p$ is the price per unit). It is known that at a price of 2 monetary units, buyers are willing to purchase no more than 8 units of the product, and at a price of 3 monetary units, no more than 6 units of the product, with the demand curve being linear.

a) What will be the equilibrium price and quantity of the product sold?

b) To increase consumption of this product, the government has introduced a per unit subsidy for its producers amounting to $s = 1$ for each unit produced. By how many units will the quantity sold increase? (14 points).

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