
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 triangle $ABC$, $A=\frac{π}{2}$, $AB=6$, $AC=4$, $D$ is the midpoint of $AB$.  
$(1)$ Find the projection vector of $\overrightarrow{CD}$ on $\overrightarrow{AC}$.  
$(2)$ If $|\overrightarrow{CP}|=1$, find the range of $\overrightarrow{PA} \cdot \overrightarrow{PB}$.

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