
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 from point $A_0$. It flies $1$ meter due north to point $A_1$. For $k \ge 1$, once the butterfly reaches point $A_k$, it turns $60^{\circ}$ clockwise and then flies $k+1$ meters straight to point $A_{k+1}$. Calculate the butterfly's distance from $A_0$ when it reaches $A_5$.

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