
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 four real numbers $-9$, $a\_1$, $a\_2$, and $-1$ that form an arithmetic sequence, and five real numbers $-9$, $b\_1$, $b\_2$, $b\_3$, and $-1$ that form a geometric sequence, find the value of $b\_2(a\_2-a\_1)=$\_\_\_\_\_\_.

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