
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 $f(x) = \sin^2x + \sin x \cos x - \frac{1}{2}$, among the following conclusions:  
① The function $f(x)$ is symmetric about $x = \frac{\pi}{8}$;  
② The function $f(x)$ is symmetric about $(-\frac{\pi}{8}, 0)$;  
③ The function $f(x)$ is increasing on the interval $(0, \frac{\pi}{8})$;  
④ The graph of $y = \frac{\sqrt{2}}{2}\cos(2x)$, when shifted to the right by $\frac{3\pi}{8}$, results in the graph of $f(x)$.  
The correct conclusion number(s) is (are) __________ .

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