
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 if \\(\neg p\\) is a sufficient but not necessary condition for \\(\neg q\\), find the range of the real number \\(m\\).

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