
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
The parabola $y = ax^2 + bx + c$ has vertex $(h, k)$ where $h$ and $k$ are positive numbers, and a $y$-intercept at $(0, -k)$. Calculate the value of $b$ if $k = 2h$.

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