
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 $f(x)= \begin{cases} x^{2}+2x+a, & x < 0 \\ \ln x, & x > 0\end{cases}$, where $a$ is a real number. Let $A(x_{1},f(x_{1}))$ and $B(x_{2},f(x_{2}))$ be points on the graph of the function, and $x_{1} < x_{2}$.  
(Ⅰ) Identify the intervals of monotonicity for the function $f(x)$.  
(Ⅱ) If the tangents to the graph of $f(x)$ at points $A$ and $B$ are perpendicular, and $x_{2} < 0$, find the minimum value of $x_{2}-x_{1}$.  
(Ⅲ) If the tangents to the graph of $f(x)$ at points $A$ and $B$ coincide, determine the range of values for $a$.

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