
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 $f\_n(x)=\sum\_{i=1}^{n}\left|x-i\right|$, where $n\in\mathbb{N}^*$.

(1) Solve the inequality: $f\_{2}(x) < x+1$;

(2) Find the minimum value of $f\_{5}(x)$.

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