
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 $\alpha \in \left(\frac{\pi}{2}, \pi\right)$ and $\sin \alpha = \frac{\sqrt{5}}{5}$, let $\vec{a} = (\cos\alpha, \sin\alpha)$ and $\vec{b} = (\cos2\alpha, \sin2alpha)$. The tasks are:  
(1) Determine whether vectors $\vec{a}$ and $\vec{b}$ are parallel.  
(2) Find the value of the dot product $\vec{a} \cdot \vec{b}$.

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