
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 function $f(x)=2\cos \left(2x+ \frac{π}{6}\right)$ ($x\in R$), four propositions are provided. The correct proposition(s) is/are \_\_\_\_\_\_.

1. The minimum positive period of the function $f(x)$ is $2π$
2. The graph of the function $f(x)$ is symmetrical about the point $\left( \frac{π}{6},0\right)$
3. The graph of the function $f(x)$ can be obtained by shifting the graph of $y=2\cos 2x$ to the left by $\frac{π}{6}$ units
4. The function $f\left(x+ \frac{π}{6}\right)$ is an odd function

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