
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 $f(x)=a^{x}$ ($a > 0$ and $a \neq 1$) has the difference between its maximum and minimum values on the interval $[-1,1]$ equal to $\frac{3}{2}$.

(Ⅰ) Find the value of the real number $a$;

(Ⅱ) If $g(x)=f(x)-f(-x)$, when $a > 1$, solve the inequality $g(x^{2}+2x)+g(x-4) > 0$.

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