
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
1. When a die (with faces numbered 1 through 6) is thrown twice in succession, find the probability that the sum of the numbers facing up is at least 10.

2. On a line segment MN of length 16cm, a point P is chosen at random. A rectangle is formed with MP and NP as adjacent sides. Find the probability that the area of this rectangle is greater than 60cm².

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