
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
Let \( A(x_{1}, y_{1}) \) and \( B(x_{2}, y_{2}) \) be any two points on the graph of the function \( f(x) = \frac{1}{2} + \log_{2} \left( \frac{x}{1-x} \right) \), and suppose \( \overrightarrow{O M} \) is the midpoint of \( \overrightarrow{O A} \) and \( \overrightarrow{O B} \). Given that 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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