
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 function $f(x)$ defined on $\mathbb{R}$ is symmetric about the point $\left(-\frac{3}{4},0\right)$ and satisfies $f(x)=-f(x+\frac{3}{2})$, with $f(-1)=1$ and $f(0)=-2$, find the value of $\sum_{k=1}^{2008}f(k)$.

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