
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 function $f(x)=m-|x-1|-|x+1|$.
- $(1)$ When $m=5$, find the solution set of the inequality $f(x) > 2$;
- $(2)$ If the graph of the function $y=x^{2}+2x+3$ always has common points with the graph of $y=f(x)$, find the range of the real number $m$.

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