
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
The function $f(x)= \begin{cases} 2x^{2},& x\in[0, \frac {1}{2}] \\ \log_{\frac {1}{4}}x,& x\in(\frac {1}{2},1] \end{cases}$ is defined on an arithmetic sequence $\{a_n\}$ with $a_1=0$ and $a_{2015}=1$. The sequence $\{b_n\}$ satisfies $b_n=f(a_{n+1})-f(a_n)$. Find the sum of the first 2014 terms of the sequence $\{b_n\}$.

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