
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 $f(x) = \lg \left( \frac{2x}{ax+b} \right)$, where $f(1) = 0$ and for $x > 0$, it always holds that $f(x) - f\left(\frac{1}{x}\right) = \lg x$.  
(1) Find the explicit formula for $f(x)$.  
(2) If the solution set of the equation $f(x) = \lg(m+x)$ is empty, determine the range of values for the real number $m$.

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