
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 points $A(\cos\alpha, \sin\alpha)$ and $B(\cos\beta, \sin\beta)$, where $\alpha, \beta$ are acute angles, and that $|AB| = \frac{\sqrt{10}}{5}$:
(1) Find the value of $\cos(\alpha - \beta)$;
(2) If $\tan \frac{\alpha}{2} = \frac{1}{2}$, find the values of $\cos\alpha$ and $\cos\beta$.

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