
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
In the Cartesian coordinate plane $(xOy)$, two acute angles $\alpha$ and $\beta$ are formed with the non-negative semi-axis of $Ox$ as the initial side. Their terminal sides intersect the unit circle at points $A$ and $B$ respectively. The vertical coordinates of $A$ and $B$ are $\frac{\sqrt{5}}{5}$ and $\frac{3\sqrt{10}}{10}$ respectively.

1. Find $\alpha - \beta$.
2. Find the value of $\cos(2\alpha - \beta)$.

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