
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
Let the sides opposite to the angles $A$, $B$, $C$ in $\triangle ABC$ be $a$, $b$, $c$ respectively, and $a+c=6$, $b=2$, $\cos B= \frac {7}{9}$.  
$(1)$ Find the values of $a$ and $c$;  
$(2)$ Find the value of $\sin (A-B)$.

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