
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, given vector $\overrightarrow{a} = (-1, 2)$, and points A$(8, 0)$, B$(n, t)$, C$(k\sin\theta, t)$ $(0 \leq \theta \leq \frac{\pi}{2})$.
(1) If $\overrightarrow{AB} \perp \overrightarrow{a}$ and $|\overrightarrow{AB}| = \sqrt{5}|\overrightarrow{OA}|$ (where $O$ is the origin), find the vector $\overrightarrow{OB}$;
(2) If vector $\overrightarrow{AC}$ is collinear with vector $\overrightarrow{a}$, when $k > 4$, and $t\sin\theta$ reaches its maximum value of 4, find $\overrightarrow{OA} \cdot \overrightarrow{OC}$.

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