
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 that point P is a moving point on the line l: x - y + 1 = 0. If there exist two points M and N on the circle C: (x-2)^2 + (y-1)^2 = 1 such that ∠MPN=60°, determine the range of the abscissa of point P.

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