
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
In the Cartesian coordinate system $xoy$, point $P(0, 1)$ lies on the curve $C: y = x^3 - x^2 - ax + b$ (where $a, b$ are real numbers). Given that the tangent line to curve $C$ at point $P$ is $y = 2x + 1$, find the value of $a + b$.

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