
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
Observe the following equations:
1<sup>3</sup>=1,
1<sup>3</sup>+2<sup>3</sup>=9,
1<sup>3</sup>+2<sup>3</sup>+3<sup>3</sup>=36,
1<sup>3</sup>+2<sup>3</sup>+3<sup>3</sup>+4<sup>3</sup>=100
...
Conjecture: 1<sup>3</sup>+2<sup>3</sup>+3<sup>3</sup>+4<sup>3</sup>+...+n<sup>3</sup>=\_\_\_\_\_\_ (n∈N*)

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