
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
There are 4 complex numbers $a+bi$, $c+di$, $e+fi$, and $g+hi$. If $b=2$, $g=-a-c-e$ and $3(a+bi+c+di+e+fi+g+hi)=2i$, find $d+f+h$.

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