
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
Let $f(x) = \sin x + \cos x$ for $x \in \mathbb{R}$.  
$(Ⅰ)$ Find the smallest positive period of the function $y = [f(x+\frac{π}{2})]^2$.  
$(Ⅱ)$ Find the maximum value of the function $y = f(x)f(x-\frac{π}{4})$ on the interval $[0, \frac{π}{2}]$.

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