
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  $n \in\mathbb{N}$ , ﬁnd all continuous functions  $f : \mathbb{R}\to \mathbb{R}$  such that for all  $x\in\mathbb{R},$ 
\[\sum_{k=0}^{n}\binom{n}{k}f(x^{2^{k}})=0. \]

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