
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 propositions:
① The function $y=2\cos^{2}\left( \frac {1}{3}x+ \frac {\pi}{4}\right)-1$ is an odd function;
② There exists a real number $\alpha$, such that $\sin\alpha+\cos\alpha= \frac {3}{2}$;
③ If $\alpha$ and $\beta$ are angles in the first quadrant and $\alpha<\beta$, then $\tan\alpha<\tan\beta$;
④ $x= \frac {\pi}{8}$ is the equation of a symmetry axis for the function $y=\sin\left(2x+ \frac {5\pi}{4}\right)$;
⑤ The graph of the function $y=\sin\left(2x+ \frac {\pi}{3}\right)$ is symmetric about the point $\left( \frac {\pi}{12},0\right)$.
Among these propositions, the correct ones are \_\_\_\_\_\_ (fill in the sequence numbers).

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