
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 the functions $f(x) = 2 - 3 \log_{2} x$ and $g(x) = \log_{2} x$.
(1) If the function $F(x) = g(\frac{1 - x}{1 + x})$, find the domain of $F(x)$ and determine its odd or even symmetry.
(2) Find the minimum value of the function $M(x) = \frac{f(x) + g(x) + |f(x) - g(x)|}{2}$.

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