
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 $f(x)=A\sin (\omega x+\varphi)+B$, where $A$, $B$, $\omega$, and $\varphi$ are real numbers, and $A > 0$, $\omega > 0$, $|\varphi| < \frac {\pi}{2}$, write a function $f(x)=$ ______ that satisfies $f(1)=2$, $f(2)= \frac {1}{2}$, $f(3)=-1$, and $f(4)=2$ (write just one possible function).

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