
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

In a box, there are 3 red, 4 gold, and 5 silver stars. Stars are randomly drawn one by one from the box and placed on a Christmas tree. What is the probability that a red star is placed on the top of the tree, no more red stars are on the tree, and there are exactly 3 gold stars on the tree, if a total of 6 stars are drawn from the box?

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