
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
Given the new operation \( a \cdot b - c \) for a triangle with vertices labeled \( a \), \( b \), and \( c \), find the sum of the results of applying this operation to three triangles and then summing the results:

1. The first triangle has numbers 2, 3, and 4.
2. The second triangle has numbers 1, 4, and 5.
3. The third triangle has numbers 6, 2, and 7.

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