
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 that $a \in (\frac{\pi}{2}, \pi)$ and $\sin a = \frac{\sqrt{5}}{5}$, find the values of:
1. $\tan(\frac{\pi}{4} + 2a)$
2. $\cos(\frac{5\pi}{6} - 2a)$

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