
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 $f(x)=e^{x}$, for any $x_{1}$, ${x_{2}} \in \mathbb{R}$, derive the range of the real number $k$ such that $\frac{f({x_{1}})-f({x_{2}})}{{x_{1}}-{x_{2}}} < |k| \cdot (f({x_{1}})+f({x_{2}}))$.

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