
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
Given the twelve Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai, and the twelve Chinese zodiac signs: Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Goat, Monkey, Rooster, Dog, Pig, they correspond to each other as follows: Zi - Rat, Chou - Ox, Yin - Tiger, Mao - Rabbit, Chen - Dragon, Si - Snake, Wu - Horse, Wei - Goat, Shen - Monkey, You - Rooster, Xu - Dog, Hai - Pig. Students made cards with the twelve Earthly Branches and the twelve Chinese zodiac signs, each in red and blue, with identical appearances. Now, three cards are randomly selected from each color. The probability that the Earthly Branches and the zodiac signs can be correctly matched is ______.

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