
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 a function $f(x) = (mx-1)e^x - x^2$,
1. If the slope of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ is $e-2$, find the intervals on which the function $f(x)$ is monotonic;
2. If the inequality $f(x) < -x^2 + mx - m$ has exactly two integer solutions for $x$, determine the range of the real number $m$.

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