
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 the function $f(x)$ is a monotonic function defined on $\mathbb{R}$, and for any $x, y \in \mathbb{R}$, it holds that $f(x+y) = f(x) + f(y)$. If the moving point $P(x, y)$ satisfies the equation $f(x^2+2x+2) + f(y^2+8y+3) = 0$, determine the maximum value of $x+y$.

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