
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) In triangle ABC, it is known that $a=\sqrt{3}$, $b=\sqrt{2}$, and $B=45^\circ$. Calculate the values of $A$, $C$, and $c$.
(2) For a geometric sequence $\{a_n\}$, given that $S_2=7$ and $S_6=91$, find the value of $S_4$.

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