
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 $f(x) = (x + b) \ln x$, the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ is parallel to the line $y = 3x$.

1. Find the value of $b$.
2. If the function $g(x) = e^x \left(\frac{f(x)}{x + 2} - 2a\right) (a \neq 0)$, and $g(x)$ is a monotonic function on the interval $(0, +\infty)$, find the range of values for the real number $a$.

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