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

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