
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 internal angles $A$, $B$, $C$ of $\triangle ABC$ be opposite to the sides of lengths $a$, $b$, $c$ respectively, and $a\cos B-b\cos A=\frac{3}{5}c$.

(Ⅰ) Find the value of $\frac{\tan A}{\tan B}$;

(Ⅱ) Find the maximum value of $\tan (A-B)$.

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