
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 that $e$ is the base of natural logarithms, let the function $f(x) = (e^x - 1)(x - 1)^k$ where $k=1, 2$. Determine the conditions under which $f(x)$ attains a local minimum or maximum at $x=1$.

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