
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 vectors $$\overrightarrow {a} = (2\cos\alpha, 2\sin\alpha)$$, $$\overrightarrow {b} = (-\sin\alpha, \cos\alpha)$$, $$\overrightarrow {x} = \overrightarrow {a} + (t^2 - 3) \overrightarrow {b}$$, $$\overrightarrow {y} = -k \overrightarrow {a} + \overrightarrow {b}$$, and $$\overrightarrow {x} \cdot \overrightarrow {y} = 0$$,  
(1) Find the expression for the function $k=f(t)$;  
(2) If $t \in [0, 4]$ and $4f(t) - \lambda(t-1) + 6 > 0$ always holds, find the range of the real number $\lambda$.

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