
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
Find the line that intersects each curve of the family of curves given by the equation \(4 x^{2}+5 y^{2}-8 m x-20 m y+24 m^{2}-20=0\) (where \(m\) is a real parameter) such that the length of the intercepted segment is equal to \(\frac{5}{3} \sqrt{5}\).

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