
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 triangle $ABC$ with vertices at $A(2,1)$, $B(3,2)$, and $C(-3,-1)$, and point $D$ is on line $BC$.
- (I) If $\overrightarrow{BC} = 2\overrightarrow{BD}$, find the coordinates of point $D$;
- (II) If $AD \perpendicular BC$, find the coordinates of point $D$.

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