
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 function \( f \), defined on the set of all real numbers, given that \( f^{2}(x+y)=f^{2}(x)+f^{2}(y) \) for any \( x \) and \( y \).

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