
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 $f(x)=-x^{2}+2x+m$.
(I) If the function $f(x)$ has exactly one zero, find the value of the real number $m$;
(II) Let $g(x)=f(x-1)$. If $g(x)$ is not monotonic on the interval $[2a,a+2]$, find the range of values for the real number $a$.

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