
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
Elective 4-1: Selected Topics in Geometric Proofs

Given the inequality $|x+3|-2x-1 < 0$, its solution set is $(x_{0},+\infty)$.

(Ⅰ) Find the value of $x_{0}$;

(Ⅱ) If the function $f(x) = |x-m|+\left| x+\frac{1}{m} \right|-x_{0}$ ($m > 0$) has a root, find the value of the real number $m$.

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