
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
In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. Among the following four statements, the correct statement(s) is/are _________. (Write down the number(s) of all correct statements.)

① If $\frac{\sin A}{a}=\frac{\cos B}{b}$, then $B=\frac{\pi }{4}$;

② If $B=\frac{\pi }{4}$, $b=2$, and $a=\sqrt{3}$, then there are two triangles that satisfy the conditions;

③ If $a$, $b$, $c$ form an arithmetic sequence, and $\sin A$, $\sin B$, $\sin C$ form a geometric sequence, then $\triangle ABC$ is an equilateral triangle;

④ If $a=5$, $c=2$, and the area of $\triangle ABC$, $S_{\triangle ABC}= 4$, then $\cos B=\frac{3}{5}$.

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