
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 the function $f(x)=|x-1|-2|x+a|$.
- $(1)$ When $a=1$, solve the inequality $f(x) > 1$ for its solution set.
- $(2)$ If the inequality $f(x) > 0$ always holds for $x \in [2,3]$, find the range of values for $a$.

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