
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
We know that adding several identical numbers can be calculated using multiplication. Today we are going to study subtracting several identical numbers. We define: $F\left(a,n\right)=\underset{\underbrace{a-a-a….-a}}{n \text{ times}}$. For example: $F(\frac{1}{2},3)=\frac{1}{2}-\frac{1}{2}-\frac{1}{2}=-\frac{1}{2}$, $F\left(-1,4\right)=\left(-1\right)-\left(-1\right)-\left(-1\right)-\left(-1\right)=2$. Based on the above information, complete the following questions:  
$(1)$ Fill in the blanks: $F\left(2,5\right)=$______, $F(-\frac{2}{3},4)=\_\_\_\_\_\_$.  
$(2)$ If $F\left(a,6\right)=2$, find the value of $a$.  
$(3)$ If a number is equal to the square of an integer, then it is called a perfect square, for example: because $1=1^{2}$, $4=2^{2}$, $100=10^{2}$, so $1$, $4$, $100$ are all perfect squares. If $|F\left(x,4\right)|$ is a perfect square, all two-digit positive integers $x$ that satisfy the condition are ______.

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