
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

A novice economist-cryptographer received a cryptogram from the ruler, which contained the next secret decree about introducing a per unit tax in a certain market. The cryptogram specified the amount of tax revenue that needed to be collected and emphasized that it would be impossible to collect a higher amount of tax revenue in this market. Unfortunately, the economist-cryptographer deciphered the cryptogram incorrectly — the digits in the tax revenue amount were determined in the wrong order. Based on these erroneous data, a decision was made to introduce a per unit tax on the consumer at a rate of 30 monetary units per unit of goods. The market supply is given by $Qs=6P-312$, and the market demand is linear. Additionally, it is known that when the price changes by one unit, the change in demand is 1.5 times less than the change in supply. After the tax was introduced, the consumer price rose to 118 monetary units.

1) Restore the market demand function.
2) Determine the amount of tax revenue collected at the chosen rate.
3) Determine the rate of the per unit tax that would achieve the ruler's decree.
4) What is the amount of tax revenue the ruler indicated to collect?

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