
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$0.3^{5} \gt \log _{3}5$, ②$\ln \sqrt{2}＜\frac{\sqrt{2}}{2}$, ③${e}^{\frac{2}{3}} \gt 2$, ④$2\ln (\sin \frac{1}{8}+\cos \frac{1}{8}) ＜ \frac{1}{4}$

Which of the above inequalities are correct? Please fill in the corresponding numbers.

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