
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 space rectangular coordinate system $Oxyz$, given points $A(0,a,1)$ and $B(-1,2,2)$.  
$(1)$ To make $\triangle OAB$ an acute triangle, find the set of all real numbers $a$ that satisfy the condition.  
$(2)$ For what value of $a$ does the area of $\triangle OAB$ reach its minimum?

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