
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
Selected Exercise 4-5: Inequality Lecture

Given $f(x)=|x+1|-|ax-1|$.

(1) When $a=1$, find the solution set of the inequality $f(x) > 1$.

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

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