
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 \( x_{1}, x_{2}, \ldots, x_{1970} \) be positive integers satisfying \( x_{1} + x_{2} + \cdots + x_{1970} = 2007 \). Determine the largest possible value of \( x_{1}^{3} + x_{2}^{3} + \cdots + x_{1970}^{3} \).

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