
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 there are two types of golden triangles, one with a vertex angle of $36^{\circ}$ and the other with a vertex angle of $108^{\circ}$, and the ratio of the side opposite the $36^{\circ}$ angle to the side opposite the $72^{\circ}$ angle in the golden triangle with a vertex angle of $36^{\circ}$ is $\frac{\sqrt{5}-1}{2}$, express $\frac{1-2\sin^{2}27^{\circ}}{2t\sqrt{4-t^{2}}}$ in terms of $t$, where $t=\frac{\sqrt{5}-1}{2}$.

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