
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 $e = 2.71828\cdots$ is the base of the natural logarithm.

(Ⅰ) Find the intervals of monotonicity for the function $f(x)$.

(Ⅱ) When $x \in \left[0, \frac{\pi}{2}\right]$, $f(x) \geqslant kx$, find the range of the real number $k$.

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