
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
A die is rolled three times. The first result is $a$, the second is $b$, and the third is $c$. Assuming each number from 1 to 6 is equally likely to appear:

1. Calculate the probability that $a b + 2 c \geq a b c$.
2. Calculate the probability that $a b + 2 c$ and $2 a b c$ are coprime.

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