
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, O is the origin. Given vector $\overrightarrow{a}=(2,1)$, point $A(1,0)$, and point $B(\cos\theta,t)$,  
(1) If $\overrightarrow{a} \parallel \overrightarrow{AB}$ and $|\overrightarrow{AB}| = \sqrt{5}|\overrightarrow{OA}|$, find the coordinates of vector $\overrightarrow{OB}$.  
(2) If $\overrightarrow{a} \perp \overrightarrow{AB}$, find the minimum value of $y=\cos^2\theta-\cos\theta+\left(\frac{t}{4}\right)^2$.

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