
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 the curve $f(x) = ax^3 + b$, the equation of the tangent line at $x=1$ is $y=3x-1$.

(1) Find the analytic expression of $y=f(x)$;  
(2) Find the equation of the tangent line of the curve passing through the point $(-1, 0)$.

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