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

1. Find the value of $\sin\alpha + \cos\alpha$.
2. Find the value of $\frac{\sin2\alpha}{\sin\alpha - \cos\alpha}$.

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