
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 the coordinates of four points A, B, C, and D are A(1, 0), B(4, 3), C(2, 4), and D(0, 2) respectively:  
(1) Determine the shape of quadrilateral ABCD and provide a proof;  
(2) Calculate $\cos\angle DAB$;  
(3) Let the real number $t$ satisfy $(\overrightarrow{AB} - t\overrightarrow{CD}) \perp \overrightarrow{OC}$, find the value of $t$.

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