
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 line \( y = kx + 1 \) intersects with the left branch of the hyperbola \( x^{2} - y^{2} = 1 \) at points \( A \) and \( B \). The line \( l \) passes through the point \( (-2, 0) \) and the midpoint of \( AB \). Find the range of values for the y-intercept \( b \) of the line \( l \).

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