
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
In an AC circuit where impedances can also be combined due to parallel connections, suppose we have \(V = 2+2i\) and two impedances \(Z_1 = 2+i\) and \(Z_2 = 4+2i\). Find the current \(I\) flowing through the circuit when the total impedance \(Z\) is calculated by the formula \(Z = \frac{Z_1 Z_2}{Z_1 + Z_2}\). Express \(I\) as a complex number.

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