
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 functions $f(x)=e^{x}\sin x$ and $g(x)=xe^{x}$.
$(1)$ Find the monotonic intervals of $f(x)$.
$(2)$ Let $h(x)=\frac{f(x)}{g(x)}$, and $x\in(0,\frac{π}{2}]$. Find the minimum value of $h(x)$.

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