
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 $\triangle ABC$, with $A(0,3)$, $B(2,2)$, and $C(-4,6)$:  
(1) Find the projection of vector $\overrightarrow{AB}$ on $\overrightarrow{AC}$.  
(2) Let $CD$ be the height from $C$ to side $AB$ of $\triangle ABC$, find the coordinates of point $D$.

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