
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
Given that in the oblique triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, $c$, and $\sin A = \cos B$.
$(1)$ Find the value of $A-B$;
$(2)$ If $a=1$, find the minimum value of $\overrightarrow{AB} \cdot \overrightarrow{AC}$;
$(3)$ If $\sin A = \cos B = \frac{3}{2} \tan C$, find the values of $A$ and $B$.

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