
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 graph of the function $f(x)$, defined on $\mathbb{R}$, is symmetric about the point $(-\frac{3}{4}, 0)$, and it satisfies $f(x) = -\frac{1}{f\left( x + \frac{3}{2} \right)}$. Given that $f(-1) = 1$ and $f(0) = -2$, find the value of $f(1) + f(2) + \ldots + f(2011)$.

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