
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
A quadratic equation is given by $x^2 + bx + \frac{1}{5}$, where $b$ is a specific negative number. Thomas rewrites this quadratic by completing the square and results in the form $(x+n)^2 + \frac{1}{20}$. Determine $b$.

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