
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 $a_{1}$, $a_{2}$, $b_{1}$, $b_{2}$ are real numbers, and $-1$, $a_{1}$, $a_{2}$, $-4$ form an arithmetic sequence, $-1$, $b_{1}$, $b_{2}$, $-8$ form a geometric sequence, find the value of $\frac {a_{2}-a_{1}}{b_{2}}$.

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