
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 $f(x)=e^{x}\sin x-a\ln (x+1)$, where $a\in \mathbb{R}$.<br/>$(Ⅰ)$ If $x=0$ is a critical point of $f(x)$, find the value of $a$;<br/>$(Ⅱ)$ If $f(x)$ has one zero in the interval $(-1,0)$ and another zero in the interval $(\frac{\pi}{4},\pi)$, find the range of values for $a$.<br/>Given data: $\frac{\sqrt{2}}{2}e^{\frac{\pi}{4}} > 1$.

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