
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 $f(x)=|x+m|+|2x-1| (m > 0)$.

(1) When $m=1$, solve the inequality $f(x)\geqslant 3$;

(2) When $x\in[m,2m^{2}]$, the inequality $\frac{1}{2}f(x)\leqslant |x+1|$ always holds true. Find the range of values for the real number $m$.

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