
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 $f$ from $\mathbb{R}$ to $\mathbb{R}$ that satisfy the following condition:

$$
\exists n \in \mathbb{N}_{\geq 2} \text{ such that } \forall x, y \in \mathbb{R}, \quad f\left(x+y^{n}\right)=f(x)+f(y)^{n}
$$

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