
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 a triangle $\triangle ABC$ with sides $a, b, c$ opposite to the angles $A, B, C$ respectively, and $\cos B = \frac{4}{5}$, $b=2$.
(Ⅰ) If $a= \frac{5}{3}$, determine the angle $A$;
(Ⅱ) If $a+c=2\sqrt{10}$, find the area $S$ of $\triangle ABC$.

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