
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 expansion of $(x+1)^2\left(x+ \frac{1}{x^{3}}\right)^n$ does not contain the term $x^2$, where $n\in\mathbb{N}^*$, and $5\leq n \leq 8$, then $n= \_\_\_\_\_\_$.

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