
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
A function $f(x)$ defined on $\mathbb{R}$ is an even function that satisfies $f(x+8) = f(x) + f(4)$ for all $x \in \mathbb{R}$ and $f(x) = 4 - x$ for $x \in [0, 4]$. Find the value of $f(2005)$.

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