
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 $O$ is the origin, the vectors $\overrightarrow{OZ_{1}}$ and $\overrightarrow{OZ_{2}}$ correspond to the complex numbers $z_{1}$ and $z_{2}$, respectively, where $z_{1}= \frac{8}{a+5}+(10-{a}^{2})$ and $z_{2}= \frac{2}{1-a}+(2a-5)$, with $a \in R$. If $\overline{z_{1}} + z_{2}$ is a real number:

(1) Find the value of the real number $a$.
(2) Determine the area of the parallelogram with $\overrightarrow{OZ_{1}}$ and $\overrightarrow{OZ_{2}}$ as adjacent sides.

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