
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 angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $$\frac{\cos B - 2\cos A}{\cos C} = \frac{2a-b}{c}$$
(1) Find the value of $\frac{a}{b}$;
(2) If angle $A$ is obtuse and $c = 3$, determine the range of values for $b$.

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