
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, $c$ respectively. Given $2c\sin B = (2a-c)\tan C$, the angle bisector of angle $C$ intersects side $AB$ at point $E$.
- Find the measure of angle $B$.
- Let the areas of triangles $\triangle BCE$ and $\triangle ACE$ be $S_{1}$ and $S_{2}$ respectively. Given the conditions $c=2$, $b=\sqrt{3}$ in case 1 and $S_{\triangle ABC}=\frac{3\sqrt{3}}{4}$, $b=\sqrt{7}$, $A>C$ in case 2, choose one of the conditions and find the value of $\frac{S_{1}}{S_{2}}$. Note: If multiple conditions are chosen and answered separately, the first answer will be scored.

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