
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
Let $a\in \mathbb{R}$, and the function $f(x) = \begin{cases} -\frac{1}{x}+a, & x<0 \\ \sqrt{x}(x-a)-1, & x>0 \end{cases}$.

(Ⅰ) When $a=2$, determine the monotonic intervals of the function $f(x)$.

(Ⅱ) If for any $x\in \mathbb{R}$, and $x\neq 0$, we have $f(x) > x-1$, find the range of values for $a$.

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