
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 $f_1(x) = \sin x + \cos x$, let $f_2(x) = f'_1(x)$, $f_3(x) = f'_2(x)$, ..., $f_n(x) = f'_{n-1}(x)$ ($n \in \mathbb{N}^*$, $n \geq 2$), then $f_1\left( \frac{\pi}{2} \right) + f_2\left( \frac{\pi}{2} \right) + \ldots + f_{2017}\left( \frac{\pi}{2} \right) = \_\_\_\_\_\_$.

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