
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 inequality $|x-m| < |x|$ has the solution set $(1, +\infty)$.  
(1) Find the value of the real number $m$;  
(2) If the inequality $$\frac {a-5}{x} < |1+ \frac {1}{x}| - |1- \frac {m}{x}| < \frac {a+2}{x}$$ holds true for $x \in (0, +\infty)$, find the range of values for the real number $a$.

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