
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
Among the following functional equations, determine which ones admit only injective, surjective, or bijective solutions:

1. $f(x+f(y))=2 f(x)+y$
2. $f(f(x))=0$
3. $f(f(x))=\sin (x)$
4. $f(x+y)=f(x) f(y)$

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