
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 $1, a_1, a_2, a_3, 9$ is an arithmetic sequence, and the sequence $-9, b_1, b_2, b_3, -1$ is a geometric sequence, find the value of $\frac{b_{2}}{a_{1}+a_{3}}$.

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