
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 $A$, $B$, $C$ are denoted as $a$, $b$, $c$ respectively. Given that $\cos A= \dfrac{4}{5}$, $\tan (A-B)= \dfrac{1}{3}$, and $b=10$:

(Ⅰ) Find the value of $\sin B$.

(Ⅱ) Find the area of triangle $ABC$.

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