
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 a function $f(x)$ on $\mathbb{R}$ that satisfies $f(4-x) = f(x)$, $f(2-x) = -f(x)$, and when $x \in [0, 2]$, $f(x) = x - 1$. Find the value of $f(2011)$.

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