
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 $a \in \left( \frac{\pi}{2}, \pi \right)$, and $\sin \frac{a}{2} + \cos \frac{a}{2} = \frac{2 \sqrt{3}}{3}$.

(Ⅰ) Find the value of $\cos a$;

(Ⅱ) If $\sin(\alpha + \beta) = -\frac{3}{5}$, with $\beta \in (0, \frac{\pi}{2})$, find the value of $\sin \beta$.

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