
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 function $f(x) = x^3 + x - 16$.

(1) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(2, -6)$;  
(2) If line $l$ is a tangent to the curve $y = f(x)$ and passes through the origin, find the equation of line $l$ and the coordinates of the tangent point.

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