
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 company is hiring two types of employees, Type A and Type B, totaling 150 people. The salary of the employees comprises a basic wage. The monthly basic wages of Type A and Type B employees are respectively 2000 yuan and 3000 yuan per person. The monthly performance-related wage of a Type A employee is directly proportional to the company's monthly profit with a proportionality constant $a$ ($a > 0$), while the monthly performance wage of a Type B employee is directly proportional to the square of the company's monthly profit with a proportionality constant $b$ ($b > 0$).
(Ⅰ) If the number of Type A employees should not exceed twice the number of Type B employees, how many people should be recruited for each of the two types so that the company's total monthly basic wage expenditure is minimized?
(Ⅱ) If the company's monthly profit is $x$ thousand yuan ($x>0$), with the average monthly wages of Type A and Type B employees denoted as $w_甲$ thousand yuan and $w_乙$ thousand yuan respectively, compare the sizes of $w_甲$ and $w_乙$. (The monthly wage is the sum of the basic wage and the performance wage.)

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