
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
Simplify the expression $\dfrac{2\cos^2\alpha - 1}{2\tan(\frac{\pi}{4}-\alpha)\sin^2(\frac{\pi}{4}+\alpha)}$.
Also, given that both $\alpha$ and $\beta$ are acute angles, and $\sin\alpha = \frac{2\sqrt{5}}{5}, \sin\beta = \frac{\sqrt{10}}{10}$, find the value of $\alpha - \beta$.

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