
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 $$A=\{y|y=\sin x-\cos(x+ \frac {\pi}{6})+m，x\in\mathbb{R}\}$$ and $$B=\{y|y=-x^2+2x，x\in[1，2]\}$$, if proposition p: $x\in A$, and proposition q: $x\in B$, and p is a necessary but not sufficient condition for q, find the range of the real number $m$.

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