
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
Determine the value of $f(8) + f(9) + f(10) + \ldots + f(2012)$, given the function $f(x)$, which is a continuous even function defined over $\mathbb{R}$. The graph of $f(x)$ is translated one unit to the right to obtain an odd function, and it is given that $f(2) = -1$.

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