
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 a sequence of positive terms $\{a_{n}\}$ with the sum of the first $n$ terms denoted as $S_{n}$, and the sequence $\{a_{n}\}$ satisfies $a_{n+1}^2=a_na_{n+2}$, if $S_{3}=13$ and $a_{1}=1$, calculate the value of $\frac{a_3+a_4}{a_1+a_2}$.

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