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

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