
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, it is known that $O(0,0)$, $A(2,x)$, $B(x-3,2)$ $(x\in\mathbb{R})$  
$(1)$ When $\overrightarrow{OA} \perp \overrightarrow{OB}$, find the value of $x$.  
$(2)$ If $\overrightarrow{OA} \cdot \overrightarrow{OB} = 6$, $\overrightarrow{OC} = \overrightarrow{OA} - \overrightarrow{OB}$, find $|\overrightarrow{OC}|$.

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