
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 has 1000 employees, and on average, each employee generates a profit of 100,000 yuan per year. To increase corporate competitiveness, it has decided to optimize the industrial structure by transferring x (x is a positive integer) employees to the tertiary industry. After the adjustment, their average annual profit per person is 10,000 yuan times $a$ ($a>0$). Meanwhile, the average annual profit per remaining employee will increase by 0.2x%.  
(1) To ensure that the total annual profit generated by the remaining employees is not less than the total annual profit generated by the original 1000 employees, what is the maximum number of employees who can be transferred to the tertiary industry?  
(2) Under the condition in (1), if the total annual profit created by the transferred employees is always less than or equal to the profit generated by the remaining employees, what is the range of values for $a$?

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