
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 an acute triangle $\triangle ABC$, it is known that the sides opposite to internal angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $\sqrt{3}(\tan A - \tan B) = 1 + \tan A \cdot \tan B$.
1. If $a^2 - ab = c^2 - b^2$, find the measures of angles $A$, $B$, and $C$.
2. Given the vectors $\overrightarrow{m}=(\sin A, \cos A)$ and $\overrightarrow{n}=(\cos B, \sin B)$, find the range of $|3\overrightarrow{m} - 2\overrightarrow{n}|$.

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