
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
Let vectors $\overrightarrow {a}=(\sin x, \sqrt {3}\cos x)$, $\overrightarrow {b}=(-1,1)$, $\overrightarrow {c}=(1,1)$ (where $x\in[0,\pi]$).

(1) If $(\overrightarrow {a}+ \overrightarrow {b})\parallel \overrightarrow {c}$, find the value of the real number $x$;  
(2) If $\overrightarrow {a}\cdot \overrightarrow {b}= \frac {1}{2}$, find the value of the function $\sin(x+ \frac {\pi}{6})$.

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