
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 $1$, $a_{1}$, $a_{2}$, and $4$ form an arithmetic sequence, and $1$, $b_{1}$, $b_{2}$, $b_{3}$, and $4$ form a geometric sequence, calculate the value of $\frac{{a_{1}+a_{2}}}{b_{2}}$.

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