
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 $ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to the angles $A$, $B$, and $C$ respectively. Given that $\frac{\pi}{3} < C < \frac{\pi}{2}$ and $\frac{b}{a - b} = \frac{\sin 2C}{\sin A - \sin 2C}$,
(1) Determine the shape of the triangle $ABC$.
(2) If $|\vec{BA} + \vec{BC}| = 2$, find the range of values for $\vec{BA} \cdot \vec{BC}$.

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