
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 two points $A(x\_1,y\_1)$ and $B(x\_2,y\_2)$ on the graph of the function $f(x)=\frac{1}{2}+\log\_2\frac{x}{1-x}$, let $M$ be the midpoint of the segment $AB$. If the x-coordinate of point $M$ is $\frac{1}{2}$, find the y-coordinate of point $M$.

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