
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) Let $S_n$ be the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$. Given $S_2 = S_6$ and $a_4 = 1$, find $a_5$.  
(2) In a geometric sequence $\{a_n\}$, if $a_4 - a_2 = 24$ and $a_2 + a_3 = 6$, find the first term $a_1$ and the common ratio $q$.

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