
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 that the horizontal and vertical coordinates of point $\left(a,b\right)$ are both elements of the set $N=\{-2,-3,-4,0,5,6\}$, if there are a total of $n$ situations where the point $\left(a,b\right)$ lies in the second quadrant, determine the value of the fifth term in the expansion of ${({\sqrt{x}+\frac{2}{x}})^n}$.

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