
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 function $f(x) = \log_2(x+1)$, when the point $(x, y)$ lies on the graph of the function $y = f(x)$, the point $\left(\frac{x}{3}, \frac{y}{2}\right)$ lies on the graph of the function $y = g(x)$.  
(1) Write the expression for the function $y = g(x)$.  
(2) Determine the range of values for $x$ when $g(x) - f(x) \geq 0$.  
(3) If the equation $f(x) - g(x) - m = 0$ has two distinct real roots, find the range of values for the real number $m$.

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