
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 $a\in\left(\frac{\pi}{2}, \pi\right)$, $\sin a=\frac{\sqrt{5}}{5}$.

(Ⅰ) Find the value of $\tan \left(\frac{\pi}{4} +2a\right)$;

(Ⅱ) Find the value of $\cos \left(\frac{5\pi}{6} -2a\right)$.

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