
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 national student loan is a credit loan subsidized by the finance department, aimed at helping college students from families with financial difficulties to pay for tuition, accommodation, and living expenses during their study period in college. The total amount applied for each year shall not exceed 6,000 yuan. A graduate from the class of 2010 at a certain university, Ling Xiao, applied for a total of 24,000 yuan in student loans during his undergraduate period and promised to pay it all back within 3 years after graduation (calculated as 36 months). The salary standard provided by the contracted unit is 1,500 yuan per month for the first year, and starting from the 13th month, the monthly salary increases by 5% until it reaches 4,000 yuan. Ling Xiao plans to repay 500 yuan each month for the first 12 months, and starting from the 13th month, the monthly repayment amount will increase by x yuan each month.  
(Ⅰ) If Ling Xiao just pays off the loan in the 36th month (i.e., three years after graduation), find the value of x;  
(Ⅱ) When x=50, in which month will Ling Xiao pay off the last installment of the loan? Will his monthly salary balance be enough to meet the basic living expenses of 3,000 yuan that month?  
(Reference data: $1.05^{18}=2.406$, $1.05^{19}=2.526$, $1.05^{20}=2.653$, $1.05^{21}=2.786$)

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