
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 the function $f(x) = \log \left( \frac{2}{x+1} - 1 \right)$ have a domain of set $A$, and the function $g(x) = -x^2 + 2x + a$ ($0 \leq x \leq 3$, $a \in \mathbb{R}$) have a range of set $B$.

(Ⅰ) Calculate the value of $f\left( \frac{1}{2015} \right) + f\left( -\frac{1}{2015} \right)$.

(Ⅱ) If $A \cap B = \emptyset$, find the range of the real number $a$.

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