
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
In his country of Milnlandia, Winnie the Pooh decided to start a company that produces honey. Winnie the Pooh sells honey only in jars, and the production cost of any jar of honey is 10 milns (the currency of Milnlandia). The inverse demand function for honey is given by \( \boldsymbol{P}=310-3 \boldsymbol{Q} \) (where \( \boldsymbol{Q} \) is the number of jars, and \( \boldsymbol{P} \) is the price per jar). There are no other honey suppliers.

a) How many jars of honey will Winnie the Pooh produce if his main goal is to maximize profit?

b) The government of Milnlandia decided to introduce a tax of \( \boldsymbol{t} \) milns per jar of honey sold by Winnie the Pooh's company. What should be the value of the tax to maximize the tax revenue for Milnlandia's budget?

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