
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 $f(x) = (k+1)x^3 - 3(k+2)x^2 - k^2 - 2k$ ($k > -1$).

(1) If the monotonic decreasing interval of $f(x)$ is $(0, 4)$, find the value of $k$;  
(2) When the value of $k$ satisfies (1), find the equation of the tangent line to the curve $f(x)$ passing through $M(1, -5)$.

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