
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) For an arithmetic sequence $\{a_n\}$ with $a_1 = \frac{3}{2}$, common difference $d = -\frac{1}{2}$, and sum of the first $n$ terms $S_n = -15$, determine the value of $n$ and $a_n$.
(2) For a geometric sequence $\{a_n\}$ with common ratio $q=2$, an equation $a_n = 96$, and the sum of the first $n$ terms $S_n = 189$, find $a_1$ and $n$.

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