
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 $f(x)=4\sin (2x- \frac {π}{3})(x∈R)$, determine the number of correct propositions:

(1) $y=f(x+ \frac {π}{6})$ is an odd function;

(2) To obtain the graph of $g(x)=4\sin 2x$, the graph of $f(x)$ only needs to be shifted to the right by $\frac {π}{3}$ units;

(3) The graph of $y=f(x)$ is symmetrical about the line $x=- \frac {π}{12}$;

(4) $y=f(x)$ is monotonically increasing on $[0, \frac {5π}{12}]$.

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