
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 $\tan 2\alpha= \frac {3}{4}$, $\alpha\in(- \frac {\pi}{2}, \frac {\pi}{2})$, $f(x)=\sin (x+\alpha)+\sin (\alpha-x)-2\sin \alpha$, and for any $x\in\mathbb{R}$, it always holds that $f(x)\geqslant 0$, find the value of $\sin (\alpha- \frac {\pi}{4})$.

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