
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 $f(x) = A\sin(\omega x + \phi)$ ($A > 0$, $\omega > 0$, $|\phi| < \pi$), the highest point D on the graph has coordinates $\left(\frac{\pi}{8}, 2\right)$, and the neighboring lowest point has coordinates $\left(\frac{5\pi}{8}, -2\right)$.
- (I) Find the expression for the function $f(x)$.
- (II) Determine the set of real numbers $x$ such that $f(x) = 1$.

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