
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 the arithmetic sequence $\{a\_n\}$, given that $d=2$, $n=15$, $a\_n=-10$, find $a\_1$ and $S\_n$;
(2) In the geometric sequence $\{a\_n\}$, given that $a\_2+a\_3=6$, $a\_3+a\_4=12$, find $q$ and $S\_{10}$.

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