
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
Consider the sequence defined recursively by \( v_1 = b > 0 \) and
\[ v_{n + 1} = -\frac{1}{2v_n + 1} \] for \( n \geq 1 \). Express \( v_{20} \) in terms of \( b \).

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