
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 $\overrightarrow{m}=(\cos \alpha- \frac{\sqrt {2}}{3},-1)$, $\overrightarrow{n}=(\sin \alpha,1)$, and $\overrightarrow{m}$ is collinear with $\overrightarrow{n}$, where $\alpha \in[-\pi,0]$.

(I) Find the value of $\sin \alpha+\cos \alpha$;

(II) Find the value of $\frac{\sin 2\alpha}{\sin \alpha-\cos \alpha}$.

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