
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
In the Cartesian coordinate plane xOy, points A(-1, 0) and B(5, 0) are given. If there exists a unique point P on circle M: (x-4)²+(y-m)²=4 such that the product of the intercepts of lines PA and PB on the y-axis is 5, find the value of the real number m.

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