
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 $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $A$, $B$, $C$ form an arithmetic sequence.  
(1) If $\overrightarrow{AB} \cdot \overrightarrow{BC} = -\frac{3}{2}$, and $b= \sqrt{3}$, find the value of $a+c$;  
(2) Find the range of values for $2\sin A - \sin C$.

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