
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 convention hosting twins and triplets had 10 sets of twins and 7 sets of triplets, all from different families. Each twin shook hands with all other twins except their siblings and with two-thirds of the triplets. Each triplet, conversely, shook hands with all other triplets except their siblings and with two-thirds of the twins. Determine the number of unique handshakes at the convention.
- **A) 800**
- **B) 850**
- **C) 900**
- **D) 922**
- **E) 950**

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