
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
There are five numbered weights, each with unique identifiers. The set includes one weight each of 5g, 3g, and 1g, and two weights of 2g. If three weights are randomly selected, what is the probability that the total mass of these three weights is 9g? (Express the result as a simplified fraction).

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