
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 $$\overrightarrow {a} = (\sin x, \cos x)$$, $$\overrightarrow {b} = (\sin x, k)$$, and $$\overrightarrow {c} = (-2\cos x, \sin x - k)$$.
(1) When $x \in [0, \frac{\pi}{4}]$, find the range of values for $|\overrightarrow {b} + \overrightarrow {c}|$;
(2) If $g(x) = (\overrightarrow {a} + \overrightarrow {b}) \cdot \overrightarrow {c}$, find the value of $k$ for which the minimum value of $g(x)$ is $-\frac{3}{2}$.

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