
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]


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Given the function $f(x)=2\sin (3x- \frac {3}{4}\pi)$, determine the truth of the following propositions:

$①$ Its minimum positive period is $\frac {2}{3}\pi$;

$②$ Its graph is obtained by translating $y=2\sin 3x$ to the left by $\frac {\pi}{4}$ units;

$③$ Its expression can be written as $f(x)=2\cos (3x+ \frac {3}{4}\pi)$;

$④$ It is a monotonically increasing function on $x\in[\frac {\pi}{12}, \frac {5}{12}\pi]$.

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