
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 fifths and sixths, respectively. Spinner A (in fifths) has numbers 2, 4, 5, 7, and 9, while Spinner B (in sixths) displays 3, 6, 7, 8, 10, and 12. If each of these spinners is spun once, what is the probability that the product of the results of the two spins will be an even number?

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