
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
Simplify the following expression:

$$
\frac{\left(\sqrt[3]{\left(r^{2}+4\right) \sqrt{1+\frac{4}{r^{2}}}}-\sqrt[3]{\left(r^{2}-4\right) \sqrt{1-\frac{4}{r^{2}}}}\right)^{2}}{r^{2}-\sqrt{r^{4}-16}}
$$

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