
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 venture capital firm is considering investing in the development of a new energy product, with estimated investment returns ranging from 100,000 to 10,000,000 yuan. The firm is planning to establish a reward scheme for the research team: the reward amount $y$ (in units of 10,000 yuan) will increase with the increase in investment return $x$ (in units of 10,000 yuan), with the maximum reward not exceeding 900,000 yuan, and not exceeding 20% of the investment return.
(I) Analyze whether the function $y = \frac{x}{150} + 2$ meets the company's requirements for the reward function model, and explain the reasons;
(II) If the company adopts the function model $y = \frac{10x - 3a}{x + 2}$ as the reward function model, determine the minimum positive integer value of $a$.

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