
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  $f: \mathbb{R} \rightarrow \mathbb{R}$  which satisfy conditions: $f(x) + f(y) \ge xy$  for all real  $x, y$  and
for each real  $x$  exists real  $y$ , such that  $f(x) + f(y) = xy$ .



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