
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
Given an increasing geometric sequence $ \{a_n\} $, the sum of its first $n$ terms is $S_n$. If $a_1 = 1$ and $2a_{n+1} + 2a_{n-1} = 5a_n$ (for $n \geqslant 2$), find $S_5$.
A) $\frac{31}{16}$ 
B) $\frac{31}{32}$ 
C) $31$ 
D) $15$

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