
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
In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and it is given that $\frac{c-b}{\sqrt{2}-a} = \frac{\sin A}{\sin B + \sin C}$  
(I) Find the magnitude of angle $B$,  
(II) Let $\overrightarrow{m}=(\sin A+\cos A,1)$, $\overrightarrow{n}=(2,\cos (\frac{\pi}{2}-2A))$, find the range of values for $\overrightarrow{m} \cdot \overrightarrow{n}$.

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