
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 $f_{1}(x)=(x^{2}+2x+1)e^{x}$, $f_{2}(x)=[f_{1}(x)]'$, $f_{3}(x)=[f_{2}(x)]'$, ..., $f_{n+1}(x)=[f_{n}(x)]'$, where $n\in\mathbb{N}^{*}$. Let $f_{n}(x)=(a_{n}x^{2}+b_{n}x+c_{n})e^{x}$, find $b_{2015}$.

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