
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 points $A(1,1)$ and $B(-1,-3)$ lie on the curve $C: y = ax^3 + bx^2 + d$ (where $a$, $b$, and $d$ are constants). If the tangents to curve $C$ at points $A$ and $B$ are parallel to each other, then the value of $a^3 + b^2 + d$ is ______.

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