
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
Let $D$ be a finite set of real numbers containing $1$, and let $y=f\left(x\right)$ be a function defined on $D$. If the graph of $y=f\left(x\right)$ rotates counterclockwise around the origin by $\frac{π}{6}$ and coincides with the original graph, then the possible values of $f\left(1\right)$ are ______ (fill in the serial number).  
① $\sqrt{3}$  
② $\frac{{\sqrt{3}}}{2}$  
③ $\frac{{\sqrt{3}}}{3}$  
④ $0$

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