
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
Point M(5,0) is given. A line is called a "cutting line" if there exists a point P on the line such that the distance |PM| equals 4. Identify all the "cutting lines" from the following options:
1. $y=x+1$
2. $y=2$
3. $y=\frac{4}{3}x$
4. $y=2x+1$.

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