
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 local government intends to encourage entrepreneurship by rewarding newly established small and micro enterprises with an annual output value between 500,000 and 5,000,000 RMB. The reward scheme follows these principles: The bonus amount $y$ (in ten thousand RMB) increases with the yearly output value $x$ (in ten thousand RMB), the bonus is no less than 700,000 RMB, and the bonus does not exceed 15% of the annual output value.
1. If an enterprise has an output value of 1,000,000 RMB and is eligible for a 90,000 RMB bonus, analyze whether the function $y=\log x + kx + 5$ (where $k$ is a constant) is in line with the government's reward requirements, and explain why (given $\log 2 \approx 0.3, \log 5 \approx 0.7$).
2. If the function $f(x) = \frac{15x - a}{x + 8}$ is adopted as the reward model, determine the minimum value of the positive integer $a$.

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