
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 the curve family \(4x^{2} + 5y^{2} - 8mx - 20my + 24m^{2} - 20 = 0\), where \(m\) is a real parameter, find the straight line such that every curve in the family intersects it in a segment of length \(\frac{5}{3}\sqrt{5}\).

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