
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 $\overrightarrow{a}=(\sin x,1)$ and $\overrightarrow{b}=(1,k)$, let $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}$.  
(Ⅰ) If the equation $f(x)=1$ about $x$ has solutions, find the range of the real number $k$;  
(Ⅱ) If $f(\alpha)= \frac {1}{3}+k$ and $\alpha\in(0,\pi)$, find $\tan \alpha$.

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