
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 a quadratic function $f\left(x\right)=x^{2}-2mx+2m^{2}-4$, where $m\in R$.<br/>$(Ⅰ)$ If the solution set of the inequality $f(2^{x})\leqslant 0$ contains exactly one element, find the value of the real number $m$.<br/>$(Ⅱ)$ If the equation $f\left(x\right)=0$ has solutions in the interval $\left(2,+\infty \right)$, let $k$ be the number of solutions. Find the possible values of $k$ and the corresponding range of real numbers for $m$.

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