
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 certain unit has 1000 employees, each creating an average annual profit of 100,000 yuan. In order to increase the competitiveness of the enterprise, it is decided to optimize the industrial structure by adjusting x (x ∈ N*) employees to engage in the tertiary industry. After the adjustment, the average annual profit per person is 10(a - 3x/500) thousand yuan (a > 0), and the remaining employees can increase their average annual profit by 0.2x%.

$(1)$ If the total annual profit created by the remaining employees is not less than the total annual profit created by the original 1000 employees, how many employees at most should be adjusted to engage in the tertiary industry?

$(2)$ If the total annual profit created by the remaining employees is not less than the total annual profit created by the original 1000 employees, and it is required that the total annual profit created by the adjusted employees does not exceed the total annual profit created 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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