
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 set $A=\{z|z=1+i+i^{2}+\cdots +i^{n}, n\in N^{*}\}$, $B=\{\omega|\omega=z_{1}\cdot z_{2}, z_{1},z_{2}\in A\}$ ($z_{1}$ can be equal to $z_{2}$), when randomly selecting an element from set $B$, the probability that the modulus of this element is $\sqrt{2}$ is __________.

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