
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 graph of the function $f(x) = \frac {1}{x+1} + x + a - 1$ is symmetric with respect to the center point $(-1, -1)$ and $g(x) = e^x + ax^2 + bx$, the tangent line at the point $(1, f(1))$ on the curve $y = f(x)$ is perpendicular to the tangent line at the point $(0, g(0))$ on the curve $y = g(x)$. Find the value of $a + b$.

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