
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 ${f_{1}}(x)=\sin x+\cos x$, denote ${f_{2}}(x)={f_{1}}(x),...,{f_{n+1}}(x)={f_{n}}(x),...,$ then ${{f_{1}}(\dfrac{\pi }{3})+{{f}_{2}}(\dfrac{\pi }{3})+{{f}_{3}}(\dfrac{\pi }{3})+... +{{f}_{2017}}(\dfrac{\pi }{3})=}$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

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