
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
Given that the line \( l \) passes through the focus of the parabola \( C: y^2 = 4x \), and the slope \( k > 2 \). The line \( l \) intersects the parabola \( C \) at points \( A \) and \( B \). The distance from the midpoint \( M \) of \( A B \) to the line \( L_m: 3x + 4y + m = 0 \) (where \( m > -3 \)) is \( \frac{1}{5} \). Find the range of values for \( m \).

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