
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 two sequences $\{a_n\}$ and $\{b_n\}$, satisfying $a_1 = 1$, and $a_n$, $a_{n+1}$ are the two roots of the function $f(x) = x^2 - b_nx + 2^n$. Find $b_{10}$.

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