
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
(1) Given a sector with radius $R$ and central angle $a$, and the perimeter of the sector is a constant value $c$, the maximum area of the sector is __________.

(2) The interval of monotonic decrease for the function $y=\sin (-2x+ \frac{\pi}{6})$ is __________.

(3) The domain of the function $y= \sqrt{16-x^{2}}+ \sqrt{\sin x}$ is __________.

(4) Consider the following statements:

① The function $y=\cos \left(\frac{2}{3}x+ \frac{\pi}{2}\right)$ is an odd function;  
② There exists a real number $x$, such that $\sin x + \cos x = 2$;  

③ If $α$ and $β$ are angles in the first quadrant and $α < β$, then $\tan α < \tan β$;  
④ $x= \frac{\pi}{8}$ is a line of symmetry 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 $\left( \frac{\pi}{12},0 \right)$.

The correct statement numbers are __________.

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