
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
For an arithmetic sequence $\{a_n\}$ with common difference $d$ and $a_n > 0$, the sum of the first $n$ terms is denoted by $S_n$. If $a_2$, $S_3$, and $a_2+S_5$ form a geometric sequence, find the value of $\frac{d}{a_1}$.

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