
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, and $f(1+x) = f(3-x)$. When $-2 \leq x \leq 0$, $f(x) = 3^x$. Let $n \in \mathbb{N}^*$ and $a_n = f(n)$, calculate the value of $a_{2011}$.

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