
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 $f(x)=|x-a|-|x+1|$, where $a\in\mathbb{R}$:
(I) When $a=1$, find the solution set for the inequality $f(x)\leqslant x^2-x$;
(II) If positive real numbers $m$, $n$ satisfy $2m+n=1$, and the inequality $f(x) \leqslant \frac{1}{m} + \frac{2}{n}$ holds for all $x$, determine the range of values for the real number $a$.

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