
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 $\cos \alpha = -\dfrac{\sqrt{5}}{5}, \tan \beta = \dfrac{1}{3}$, with $\pi < \alpha < \dfrac{3\pi}{2}$ and $0 < \beta < \dfrac{\pi}{2}$.
$(1)$ Find the value of $\sin(\alpha - \beta)$;
$(2)$ Find the value of $(\alpha - \beta)$.

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