
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 crawling from point $Q_0$. It moves $2$ inches due north to point $Q_1$. For $k \ge 1$, once the bug reaches point $Q_k$, it turns $45^{\circ}$ counterclockwise and then moves $k+2$ inches straight to point $Q_{k+1}$. Calculate the distance from $Q_0$ to $Q_{100}$ in inches.

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