
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
Find the least number  $ c$  satisfyng the condition  $\sum_{i=1}^n {x_i}^2\leq cn$   
and all real numbers  $x_1,x_2,...,x_n$  are greater than or equal to  $-1$  such that  $\sum_{i=1}^n {x_i}^3=0$ 

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