
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 bag contains 4 purple, 3 orange, and 5 green chips. If the 12 chips are randomly drawn from the bag, one at a time and without replacement, what is the probability that the chips are drawn in such a way that the 4 purple chips are drawn consecutively, the 3 orange chips are drawn consecutively, and the 5 green chips are drawn consecutively, with the condition that the purple chips must be drawn last? Express your answer as a common fraction.

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