
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
An innovative team plans to develop a new product, which, according to market research, is estimated to bring in a profit ranging from 100,000 to 100,000,000 yuan. They intend to establish a reward scheme where the bonus \(y\) (in 10,000 yuan) increases with the profit \(x\) (in 10,000 yuan), with two conditions: the bonus should not exceed 90,000 yuan and should not exceed 20% of the profit.
 
(1) If a function \(y=f(x)\) is used to model the reward scheme, describe using mathematical language the team's basic requirements for the model \(f(x)\), and analyze whether \(y= \frac {x}{150}+2\) satisfies the team's reward function requirements, explaining the reasons;

(2) If the team uses the model function \(f(x)= \frac {10x-3a}{x+2}\) as the reward function, determine the minimum positive integer value of \(a\).

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