
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 functions $f(x)$ and $g(x)$ on $\mathbb{R}$ such that $f(x) = -f(-x)$ and $g(x) = g(x + 2)$. Given that $f(-1) = g(1) = 3$ and $g(2nf(1)) = nf(f(1) + g(-1)) + 2$ for $n \in \mathbb{N}$, find the value of $g(-6) + f(0)$.

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