
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 $f(x)$ is an even function, where $x \in \mathbb{R}$, and if the graph of $f(x)$ is translated one unit to the right to obtain an odd function, and $f(2) = -1$, calculate the value of $f(1) + f(2) + f(3) + \ldots + f(2011)$.

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