
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 the odd positive integers  $n$  such that there are  $n$  odd integers  $x_1, x_2,..., x_n$  such that  $$ x_1^2+x_2^2+...+x_n^2=n^4 $$  

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