
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 $\overrightarrow{a}=k\sin \theta \overrightarrow{e_{1}}+(2-\cos \theta )\overrightarrow{e_{2}}$ and $\overrightarrow{b}=\overrightarrow{e_{1}}+\overrightarrow{e_{2}}$, with $\overrightarrow{a}//\overrightarrow{b}$, where $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are the unit vectors along the $x$-axis and $y$-axis respectively, and $\theta \in (0,\pi)$.

 (1) Find the relationship between $k$ and $\theta$:

(2) Find the minimum value of $k=f(\theta)$.

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