
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 $z_{1}= \frac{16}{a+5} -(10-a^{2})i$ and $z_{2}= \frac{2}{1-a} +(2a-5)i$, where $a\in\mathbb{R}$ and $i$ is the imaginary unit. If $z_{1}+z_{2}$ is a real number.  
(Ⅰ) Find the value of the real number $a$;  
(Ⅱ) Find the value of $\overline{z_{1}} \cdot z_{2}$.

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