
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 that $a > 0$, $b > 0$, $c > 0$, and the function $f(x)=|x+a|+|x-b|+c$.

(1) When $a=b=c=1$, find the solution set for the inequality $f(x) > 5$.

(2) If the minimum value of $f(x)$ is $5$, find the value of $a+b+c$ and the minimum value of $\frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$.

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