
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$  defined in the set of rational numbers and taking their values in the same set such that the equation  $ f(x + y) + f(x - y) = 2f(x) + 2f(y)$  holds for all rational numbers  $x$  and  $y$ .

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