
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 $16$ belts characterized by their types: B, G, G, L, L, L, P, P, P, P, R, R, R, R, S, S. If three belts and three buckles fall into a bag, with buckles being either made of silver or gold (indistinguishable among their kind) with two gold and four silver available, how many distinct collections of items could be put in the bag considering all B’s, G's, and S's (belt type and silver buckles) are indistinguishable?

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