
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 $f(x)=|x+1-2a|+|x-a^{2}|$, $g(x)=x^{2}-2x-4+ \dfrac {4}{(x-1)^{2}}$

(Ⅰ) If $f(2a^{2}-1) > 4|a-1|$, find the range of the real number $a$;

(Ⅱ) If there exist real numbers $x$, $y$, such that $f(x)+g(y)\leqslant 0$, find the range of the real number $a$.

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