
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
When a red die and a blue die are thrown at the same time, let event $M$ be "the number of points facing up on the red die is a multiple of 3", and $N$ be "the sum of the points on both dice is greater than 8". Calculate $P(N|M)$.

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