
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
Let the sequence \(b_1, b_2, b_3, \dots\) be defined such that \(b_1 = 24\), \(b_{12} = 150\), and for all \(n \geq 3\), \(b_n\) is the arithmetic mean of the first \(n - 1\) terms. Find \(b_2\).

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