
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 $f(x)=2\sin (2x+ \frac {π}{3})$, determine the correct propositions:
  1. $y=f(x+ \frac {π}{3})$ is an odd function.
  2. To obtain the graph of $g(x)=2\cos 2x$, the graph of $f(x)$ can be shifted left by $\frac {π}{12}$ units.
  3. The graph of $y=f(x)$ is symmetric about the line $x= \frac {π}{12}$.
  4. $y=f(|x|)$ is a periodic function.

Provide the sequence number(s) of the correct proposition(s).

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