
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 that the function $$f(x) = \log_{2}\left(\frac{1 - ax}{1 + x}\right)$$ is an odd function.

(1) Find the value of the real number $a$;
(2) Let the function $g(x) = f(x) - \log_{2}(mx)$. Determine if there exists a non-zero real number $m$ such that the function $g(x)$ has exactly two zeros. If it exists, find the range of values for $m$; if not, provide the reason.

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