
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
Given is a positive integer  $n \geq 2$ . Determine the maximum value of the sum of natural numbers  $k_1,k_2,...,k_n$  satisfying the condition: $k_1^3+k_2^3+ \dots +k_n^3 \leq 7n$ .

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