
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 $f(x) = \log_2 \left(\frac{x+a}{x-1}\right)$ (where $a > 0$) is an odd function.  
(1) Find the value of the real number $a$.  
(2) If $x \in (1, 4]$, and $f(x) > \log_2 \left(\frac{m}{x-1}\right)$ always holds, find the range of values of the real number $m$.

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