
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 the function $f(x)=\sin (ωx+φ)$, where $ω > 0$ and $-\frac{π}{2} ≤ φ ≤ \frac{π}{2}$, the distance between a highest point and its adjacent lowest point on the graph is $2 \sqrt{2}$. Furthermore, the function passes through the point $(2, -\frac{1}{2})$. Determine the function $f(x)=$\_\_\_\_\_\_\_\_.

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