
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 the complex plane, the points \\(A\\), \\(B\\), and \\(C\\) correspond to the complex numbers \\(i\\), \\(1\\), and \\(4+2i\\) respectively. A parallelogram \\(ABCD\\) is formed in the counterclockwise direction from \\(A\\) to \\(B\\) to \\(C\\) to \\(D\\). Then, the magnitude of \\(| \overrightarrow{BD}|=\\) \_\_\_\_\_\_.

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