
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
Solve the following two questions:  
(I) Given a complex number $z=- \frac {1}{2}+ \frac { \sqrt {3}}{2}i$, its conjugate is $\overline {z}$. Find $| \frac {1}{z}|+(\overline {z})^{2}$.  
(II) For complex numbers $z_{1}=2a+1+(1+a^{2})i$ and $z_{2}=1-a+(3-a)i$, where $a \in \mathbb{R}$, if $z_{1}+ \overline {z_{2}}$ is a real number, find the value of $a$.

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