
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 $f(x)=|x-2|-|2x+1|$,

(I) Solve the inequality $f(x)\leqslant 0$;

(II) For all $x\in R$, the inequality $f(x)-2m^{2}\leqslant 4m$ always holds. Find the range of values for the real number $m$.

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