
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 two-dimensional rectangular coordinate system, given the vector $\overrightarrow{a}=(-1,2)$, and points $A(8,0)$, $B(n,t)$, $C(k\sin θ,t)(0≤θ≤\frac {π}{2})$.
(1) If $\overrightarrow{AB} \perp \overrightarrow{a}$, and $|\overrightarrow{AB}|= \sqrt {5}|\overrightarrow{OA}|(O$ is the origin$)$, find the vector $\overrightarrow{OB}$;
(2) If the vector $\overrightarrow{AC}$ is collinear with the vector $\overrightarrow{a}$, when $k > 4$, and $t\sin θ$ takes the maximum value $4$, find $\overrightarrow{OA}\cdot \overrightarrow{OC}$.

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