
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 $f(x) = 2x^3 - 3x^2 + a$ has a maximum value of 6.  
(1) Find the value of $a$;  
(2) When $x \in [-2, 2]$, and $t \in [-1, 1]$, $f(x) \geq kt - 25$ always holds, find the range of values for $k$.

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