
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
Find the infinite sum of \(\frac{1^{3}}{3^{1}}+\frac{2^{3}}{3^{2}}+\frac{3^{3}}{3^{3}}+\frac{4^{3}}{3^{4}}+\cdots\).

求 \(\frac{1^{3}}{3^{1}}+\frac{2^{3}}{3^{2}}+\frac{3^{3}}{3^{3}}+\frac{4^{3}}{3^{4}}+\cdots\) 無限項之和。

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