
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
Consider the set V of all planar vectors, and let a mapping f: V→R have property P if for any vectors a=(x₁, y₁)∈V, b=(x₂, y₂)∈V, and any scalar λ∈R, it satisfies $f(λa+(1-λ)b)=λf(a)+(1-λ)f(b)$. Here are the given mappings:
① $f_1$: V→R, $f_1(m)=x-y$, for m=(x, y)∈V;
② $f_2$: V→R, $f_2(m)=x^2+y$, for m=(x, y)∈V;
③ $f_3$: V→R, $f_3(m)=x+y+1$, for m=(x, y)∈V.
The mapping(s) that possess the property P are marked by the number(s) __________.

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