
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
Two spinners are divided into halves and fifths, respectively. When each of these spinners is spun once, what is the probability that the product of the results of the two spins will be a prime number? The numbers on the halves spinner are 4 and 6, and the numbers on the fifths spinner are 2, 3, 5, 7, and 11.

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