
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 begins its journey from point $Q_0$. It flies $2$ inches due north to point $Q_1$. For $k \ge 1$, once the butterfly reaches point $Q_k$, it turns $45^\circ$ clockwise and then flies $2k+1$ inches straight to point $Q_{k+1}$. Determine the distance from $Q_0$ to $Q_{1007}$, in inches.

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