
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 system $(xOy)$, two acute angles $\alpha$ and $\beta$ are formed with the $Ox$ axis as the initial side. Their terminal sides intersect the unit circle $(O)$ at points $A$ and $B$ respectively, with the horizontal coordinates of $A$ and $B$ being $\frac{\sqrt{2}}{10}$ and $\frac{2\sqrt{5}}{5}$ respectively.
(I) Find the value of $\cos(\alpha - \beta)$;
(II) If point $C$ is a point on the unit circle $(O)$ different from $A$ and $B$, and the angle between vectors $\overrightarrow{OC}$ and $\overrightarrow{OA}$ is $\frac{\pi}{4}$, find the coordinates of point $C$.

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