
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
Consider $n$ which is a multiple of $6$. Calculate the sum $t=1+2i+3i^2+\cdots+(n+1)i^{2n}$, where $i=\sqrt{-1}$.
A) \(6i - 7\)
B) \(7i + 6\)
C) \(6 - 7i\)
D) \(12i\)

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