
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 $f(2+x) = f(2-x)$ for all $x$, if $f(x) = 2^x$ when $-2 \leq x \leq 0$, let $n \in \mathbb{N}^*$, and let $a_n = f(n)$, find the value of $a_{2013}$.

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