
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
Assume the function $f(x) = xe^{kx}$ where $k \neq 0$.
1. Find the equation of the tangent line to the curve $y = f(x)$ at the point $(0, f(0))$.
2. Determine the intervals where the function $f(x)$ is monotonic.
3. If the function $f(x)$ is monotonically increasing in the interval $(-1, 1)$, find the range of values for $k$.

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