
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 power function $f(x)=\left( \frac{1}{x}\right)^{3+2m-m^{2}}$ ($m\in\mathbb{Z}$) is a monotonically decreasing function on $(0,+\infty)$, and it is an even function.

(Ⅰ) Find the explicit formula for $f(x)$;

(Ⅱ) If $a\in\mathbb{R}$, discuss the parity of $F(x)=af(x)+(a-2)x^{5}f(x)$ and explain the reasons.

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