
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
Call a three-digit number  $\overline{ABC}$   $\textit{spicy}$  if it satisfies  $\overline{ABC}=A^3+B^3+C^3$ . Compute the unique  $n$  for which both  $n$  and  $n+1$  are  $\textit{spicy}$ .

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