
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  $f: \mathbb{R} \rightarrow \mathbb{R}$  such that  $$ f(x^2 + y) \ge (\frac{1}{x} + 1)f(y) $$  holds for all  $x \in \mathbb{R} \setminus \{0\}$  and all  $y \in \mathbb{R}$ .


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