
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 box holds 4 green, 3 orange, and 5 blue pencils. If the 12 pencils are randomly selected from the box, one at a time and without replacement, what is the probability that the pencils are selected such that the 4 green pencils are selected consecutively, the 3 orange pencils are selected consecutively, and the 5 blue pencils are selected consecutively, but not necessarily in the green-orange-blue order? Express your answer as a common fraction.

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