
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 sets $A={z|z=1+i+i^{2}+…+i^{n},n∈N^{}}$ and $B={ω|ω=z_{1}⋅z_{2},z_{1}, z_{2}∈A}$, where $(z_{1}$ can be equal to $z_{2})$, what is the probability that the modulus of an element randomly selected from set $B$ is $\sqrt{2}$?

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