
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 $f(x)=\sin x$, $x\in R$.  
$(Ⅰ)$ Given that $\theta \in [0,2\pi)$, and the function $f(x+\theta)$ is an even function, find the value of $\theta$;  
$(Ⅱ)$ Find the range of the function $y=[f(x+\frac{π}{12})]^{2}+[f(x+\frac{π}{4})]^{2}$.

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