
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 $a, b, c$ are opposite to angles $A, B, C$ respectively, and $a > c$. If the area of $\triangle ABC$ is $2\sqrt{2}$, $\sin(A-B) + \sin C = \frac{2}{3}\sin A$, and $b=3$,

(Ⅰ) Find the value of $\cos B$;

(Ⅱ) Find the values of sides $a$ and $c$.

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