
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:  
$1^3 = 1$,  
$1^3 + 2^3 = 9$,  
$1^3 + 2^3 + 3^3 = 36$,  
$1^3 + 2^3 + 3^3 + 4^3 = 100$  
...  
Conjecture: $1^3 + 2^3 + 3^3 + 4^3 + \ldots + n^3 = \_\_\_\_\_\_$ ($n \in \mathbb{N^*}$).

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