
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 the parabola $E$: $x^{2}=4y$ with focus $F$, and point $P(a,0)$ on the x-axis.  
$(1)$ Draw line $l$ through point $P$ that is tangent to $E$, find the equation of the tangent line $l$;  
$(2)$ If there exists a line $l'$ through point $F$ intersecting the parabola at points $A$ and $B$, and the angles of inclination of lines $PA$ and $PB$ are complementary, find the range of the real number $a$.

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