
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
Let the sum of the coefficients of the expansion of the binomial $(3 \sqrt[3]{x} + \frac{1}{x})^{n}$ be $P$, and the sum of all the binomial coefficients be $S$. If $P + S = 272$, then calculate the value of $n$.

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