
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
Define an even function on $\mathbb{R}$ that satisfies $f\left( \frac{3}{2}+x\right)=f\left( \frac{3}{2}-x\right)$ and $f(-1)=1$, $f(0)=-2$. Then, find the value of $\displaystyle \sum_{k=1}^{2014} f(k)$.

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