
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
Given the sets $M=\{f(x) | f(-x)=f(x), x\in\mathbb{R}\}$; $N=\{f(x) | f(-x)=-f(x), x\in\mathbb{R}\}$; $P=\{f(x) | f(1-x)=f(1+x), x\in\mathbb{R}\}$; $Q=\{f(x) | f(1-x)=-f(1+x), x\in\mathbb{R}\}$. If $f(x)=(x-1)^3$ for $x\in\mathbb{R}$, identify the correct sequence number indicating which set $f(x)$ belongs to:

1. $f(x) \in M$
2. $f(x) \in N$
3. $f(x) \in P$
4. $f(x) \in Q$

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