
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 $\cos 75^{\circ}$ is a zero of the function $f(x)=a_{4}x^{4}+a_{3}x^{3}+a_{2}x^{2}+a_{1}x+a_{0}$ where $a_{4}$, $a_{3}$, $a_{2}$, $a_{1}$, $a_{0} \in \mathbb{Z}$ and $a_{4} \neq 0$, find $f(\sin 75^{\circ})$.

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