
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
For real numbers  $a,\ b$  with  $0\leq a\leq \pi,\ a<b$ , let  $I(a,\ b)=\int_{a}^{b} e^{-x} \sin x\ dx.$ Determine the value of  $a$  such that  $\lim_{b\rightarrow \infty} I(a,\ b)=0.$ 

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