
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 that the sequence $\{a_n\}$ is an arithmetic sequence, and the sum of its first $n$ terms is $S_n$, and $a_1 a_2 a_3 = 15$ and $\frac{3}{S_1 S_3} + \frac{15}{S_3 S_5} + \frac{5}{S_5 S_1} = \frac{3}{5}$, find the value of $a_2$.

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