
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 geometric sequence $\left\{ a_{n} \right\}$ with the sum of the first $n$ terms as $S_{n}$, and $a_{1}+a_{3}= \frac{5}{2}$, $a_{2}+a_{4}= \frac{5}{4}$, find $\frac{S_{3}}{a_{3}}$.

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