
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 all functions  $f:[0, \infty) \to [0,\infty)$ , such that for any positive integer  $n$  and and for any non-negative real numbers  $x_1,x_2,\dotsc,x_n$ \[f(x_1^2+\dotsc+x_n^2)=f(x_1)^2+\dots+f(x_n)^2.\]

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