
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
Suppose \( \triangle \) represents $a + b - 2c$ where $a$, $b$, and $c$ are the numbers at the vertices of the triangle. If \( T_1 \) is the result for the first triangle with numbers 3, 4, and 5 and \( T_2 \) is the result for the second triangle with numbers 6, 8, and 2, calculate $2T_1 + 3T_2$.

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