
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. Given vectors $\overrightarrow{p} = (2\sin A, \cos(A-B))$ and $\overrightarrow{q} = (\sin B, -1)$, and $\overrightarrow{p} \cdot \overrightarrow{q} = \frac{1}{2}$.  
(Ⅰ) Find the magnitude of angle $C$;  
(Ⅱ) If $c = \sqrt{3}$, find the range of values for $b-a$.

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