
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

Determine all functions from $\mathbb{R}$ to $\mathbb{R}$ satisfying:

$$
\forall(x, y) \in \mathbb{R}^{2}, f\left(x^{42^{42}}+y\right)=f\left(x^{3}+2 y\right)+f\left(x^{12}\right)
$$

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