
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 $b_1, b_2, \dots$ be a sequence for which $b_1 = 3$, $b_2 = 8$, and $b_n = \frac{b_{n-1} + b_{n-2}}{2}$ for each positive integer $n \ge 3$. What is $b_{2023}$?

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