
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 a function $f(x)$ defined on $\mathbb{Z}$, for any $x, y \in \mathbb{Z}$, it satisfies $f(x+y)+f(x-y)=4f(x)f(y)$ and $f(1)= \dfrac {1}{4}$. Find the value of $f(0)+f(1)+f(2)+\ldots+f(2017)$.

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