
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 the real numbers $a_1, a_2, b_1, b_2, b_3$ such that the sequence 1, $a_1, a_2, 9$ forms an arithmetic progression, and the sequence 1, $b_1, b_2, b_3, 9$ forms a geometric progression, find the value of $\frac{b_2}{a_1+a_2}$.

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