
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 that the odd function $y=f(x)$ defined on $\mathbb{R}$ satisfies $f(1+x)=f(1-x)$ for any real number $x$, and $f(x)=4^{x}-1$ when $x\in[0,1]$, find the value of $f\left[\sum\limits_{i=0}^{2017}f(i)\right]$.

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