
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 $f_{1}(x)=\sin x+\cos x$,  
$f_{2}(x)=f_{1}'(x)$,  
$f_{3}(x)=f_{2}'(x)$,  
…  
$f_{n}(x)=f_{n-1}'(x)$, … $(n\in\mathbb{N}^*, n\geqslant 2)$.  
Find the value of $f_{1}\left( \frac{\pi}{4}\right)+f_{2}\left( \frac{\pi}{4}\right)+…+f_{2016}\left( \frac{\pi}{4}\right)$.

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