
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 $$\overrightarrow {a} = (2 + \sin x, 1)$$, $$\overrightarrow {b} = (2, -2)$$, $$\overrightarrow {c} = (\sin x - 3, 1)$$, and $$\overrightarrow {d} = (1, k)$$ (where $x \in \mathbb{R}$, $k \in \mathbb{R}$).  
(1) If $x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ and $$\overrightarrow {a}$$ is parallel to ($$\overrightarrow {b}$$ + $$\overrightarrow {c}$$), find the value of $x$;  
(2) If the function $f(x) = \overrightarrow {a} \cdot \overrightarrow {b}$, find the minimum value of $f(x)$.

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