
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 $y = x^2 + bx + c$ intersects the positive half of the x-axis at points A and B, and intersects the y-axis at point C. The length of segment AB is 1, and the area of $\triangle ABC$ is 1. Find the value of $b$.

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