
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 $$f(x)=\log_{\frac{1}{2}} \frac{1-ax}{x-1}$$ be an odd function, where $a$ is a constant.  
(1) Find the value of $a$;  
(2) If for every $x$ value in the interval $[3, 4]$, the inequality $$f(x) > \left(\frac{1}{2}\right)^x + m$$ always holds, find the range of values for the real number $m$.

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