
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 $f(x)=-x^{2}+2|x-a|$.
(I) If the function $y=f(x)$ is an even function, find the value of $a$;
(II) If $a= \frac {1}{2}$, find the interval where the function $y=f(x)$ is monotonically increasing;
(III) When $a > 0$, if the inequality $f(x-1)\geqslant 2f(x)$ holds for any $x\in[0,+\infty)$, find the range of values for the real number $a$.

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