
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
Conduct an experiment by throwing 2 dice, and denote the point P with the coordinates $(x, y)$, where $x$ represents the number shown on the first die, and $y$ represents the number shown on the second die.  
(I) Find the probability that point P lies on the line $y = x$.  
(II) Find the probability that point P does not lie on the line $y = x + 1$.  
(III) Find the probability that the coordinates of point P $(x, y)$ satisfy $16 < x^2 + y^2 \leq 25$.

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