
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 $f(x)=|2x-a|-|x+1|(a\in \mathbb{R})$.

$(1)$ When $a=1$, solve the inequality $f(x) > 2$;

$(2)$ If the inequality $f(x)+|x+1|+x > a^{2}-\frac{1}{2}$ always holds for $x\in \mathbb{R}$, find the range of the real number $a$.

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