
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 sum of the coefficients of the expansion of $(\frac{3}{x}-\sqrt{x})^n$ is $512$. Find:<br/>
$(1)$ The coefficient of the term containing $x^{3}$ in the expansion;<br/>
$(2)$ The constant term in the expansion of $(1+\frac{1}{x})(2x-1)^n$.

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