
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
The semi-latus rectum of a parabola intersects with a hyperbola of the form ${x}^{2}-{y}^{2}={a}^{2}$ at points $A$ and $B$. The distance between these points is $4\sqrt{3}$. Determine the length of the real axis of the hyperbola.

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