
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
22. Given $f(x) = |x+1| - |ax-1|$.  
(1) When $a=1$, solve the inequality $f(x) > 1$;  

(2) If the inequality $f(x) > x$ holds for $x \in (0,1)$, find the range of $a$.

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