
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
With the help of Morgiana, Alibaba escaped danger and defeated the bandits. Alibaba plans to select 10 gems from 9 red, 5 blue, and 6 green gems (the only difference between the gems is their color) to give to the brave and clever Morgiana. Among these gems, there must be at least 2 red gems, at least 2 blue gems, and no more than 3 green gems. How many ways can Alibaba choose the gems?

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