
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
(The full score of this question is 12 points) Given the function $f(x) = kx^3 - 3(k + 1)x^2 - 2k^2 + 4$, if the decreasing interval of $f(x)$ is $(0,4)$.  
(1) Find the value of $k$;  
(2) For any $t \in [-1,1]$, the equation $2x^2 + 5x + a = f(t)$ always has real roots, find the range of the real number $a$.

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