
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 bug starts moving from point $Q_0$. It moves $1$ inch directly north to point $Q_1$. For $k \ge 1$, once the bug reaches point $Q_k$, it turns $45^{\circ}$ counterclockwise and then moves $k+1$ inches straight to point $Q_{k+1}$. When the bug reaches $Q_8$, how far from $Q_0$ is it, in inches?

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