
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 two points M(-5, 0) and N(5, 0), if there exists a point P on the line such that |PM| - |PN| = 6, then this line is called a "harmonic line". Among the following lines: ①y=x-1; ②y=-$\frac{2}{3}$x; ③y=$\frac{5}{3}$x; ④y=2x+1. The ones that are "harmonic lines" are \_\_\_\_\_\_ . (Fill in the serial numbers of all correct answers)

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