
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 that the approximate value of pi can be expressed as $4\sin 52^{\circ}$ and $\frac{{355}}{{113}}$, calculate $\frac{{2\pi\sqrt{16-{\pi}^2}-8\sin44^{\circ}}}{{\sqrt{3}-2\sqrt{3}\sin^2 22^{\circ}}}$.

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