
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 $f(x) = alnx - bx - 3$, the equation of the tangent line at $x = 1$ is $x + y + 4 = 0$.

1. Find the values of real numbers $a$ and $b$.
2. If the function $g(x) = bx^{3} + \frac{x^{2}}{2} [a - 2f'(x)]$ has a local extremum in the interval $(m - 1, 2m + 1)$, find the range of real number $m$.

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