
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 hyperbola $C: \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{12}=1(a>0)$, a line $l$ passing through its right focus $F$ intersects the hyperbola $C$ at points $A$ and $B$, with $|AB|=16$. If there are $4$ such lines $l$, then the range of real number $a$ is ______.

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