
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 to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. It is given that $a\sin A=4b\sin B$ and $ac= \sqrt {5}(a^{2}-b^{2}-c^{2}).$

(Ⅰ) Find the value of $\cos A$;

(Ⅱ) Find the value of $\sin (2B-A).$

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