
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 a triangle $△ABC$ with angle $B$ as an obtuse angle, and the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Let $\overrightarrow{m}=(a,2b)$, $\overrightarrow{n}=(\sqrt{3},-\sin A)$, and $\overrightarrow{m}\perp \overrightarrow{n}$.

(1) Find the size of angle $B$;  
(2) Find the range of values for $\cos A + \cos C$.

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