
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
Let the function $f(x)=xe^{kx} (k\neq 0)$.

(Ⅰ) Find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$;

(Ⅱ) Determine the intervals of monotonicity for the function $f(x)$;

(Ⅲ) If the function $f(x)$ is strictly increasing in the interval $(-1,1)$, find the range of feasible values for $k$.

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