
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 $f(x) = \sin^2x + \sin^2(x+\alpha) + \sin^2(x+\beta)$, where $\alpha, \beta$ are constants that satisfy $0 \leq \alpha \leq \beta \leq \pi$  
(1) If $\alpha= \frac {\pi}{4}, \beta= \frac {3\pi}{4}$, find the minimum value of the function $f(x)$;  
(2) Is it possible for $f(x)$ to be a constant function? If possible, find the values of $\alpha, \beta$ when $f(x)$ is a constant function. If not possible, explain why.

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