
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 following five propositions:
① The function $y=2\sin(2x- \frac {\pi}{3})$ has a symmetry axis at $x= \frac {5\pi}{12}$;
② The graph of the function $y=\tan x$ is symmetric about the point $\left( \frac {\pi}{2}, 0\right)$;
③ The sine function is increasing in the first quadrant;
④ If $\sin(2x_{1}- \frac {\pi}{4})=\sin(2x_{2}- \frac {\pi}{4})$, then $x_{1}-x_{2}=k\pi$, where $k\in \mathbb{Z}$.
Among these four propositions, the correct ones are __________ (Fill in the serial numbers of the correct propositions).

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