
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 $D$ of its graph has coordinates $(\frac{\pi}{8},2)$, and the lowest point adjacent to $D$ has coordinates $(\frac{5\pi}{8},-2)$.

(Ⅰ) Find the analytical expression of the function $f(x)$;

(Ⅱ) Find the set of real numbers $x$ that satisfy $f(x)=1$.

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