
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 the geometric sequence $\{a\_n\}$,

(1) If $q=2$, $S\_4=1$, find $S\_8$;

(2) If $a\_1+a\_3=10$, $a\_4+a\_6=\frac{5}{4}$, find $a\_4$ and $S\_5$.

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