
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
A butterfly starts at point $B_0$ (the origin). It flies $1$ inch due North to point $B_1$. From $j \ge 1$, once the butterfly reaches point $B_j$, it turns $45^\circ$ counterclockwise and then flies $j+1$ inches straight to point $B_{j+1}$. Calculate the point $B_8$ in the complex plane, and determine how far the butterfly is from point $B_0$ in inches.

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