
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 $f(x)=e^{x}\sin x$, where $x\in\mathbb{R}$, and $e=2.71828…$ is the base of the natural logarithm, when $x\in\left[0, \frac{\pi}{2}\right]$, determine the range of the real number $k$ such that the graph of the function $y=f(x)$ is not below the line $y=kx$.

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