
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
Given the function $f(x) = (a-\frac{1}{2})x^2 + \ln x$ ($a \in \mathbb{R}$):
1. If the tangent line of the function $f(x)$ at point $(1, f(1))$ is given by the equation $2x + y + b = 0$, find the values of $a$ and $b$;
2. If the graph of the function $f(x)$ is always below the line $y = 2ax$ on the interval $(1, +\infty)$, determine the range of values for $a$.

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