
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) = sin(x), where x belongs to the set of real numbers.
(I) Given θ belongs to [0, 2π), if the function f(x + θ) is an even function, find the value of θ.
(II) Find the range of the function y = [f(x + $\frac {π}{12}$)]<sup>2</sup> + [f(x + $\frac {π}{4}$)]<sup>2</sup>.

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