
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 that $\cos\alpha = -\frac{3}{5}$, and $\alpha \in (\pi, 2\pi)$.
1. Find the value of $\sin 2\alpha$.
2. If the vertex of angle $\beta$ coincides with the origin of the coordinate, the initial side coincides with the positive half of the x-axis, and the terminal side passes through the point $(3, -1)$, find the value of $\tan(\alpha - \beta)$.

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