
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
Aaron the ant starts at the origin $p_0=(0,0)$ facing east and walks one unit to $p_1=(1,0)$. For $n=1,2,3,\dots$, immediately upon arriving at $p_n$, if Aaron can turn $90^\circ$ left and walk two units to an unvisited point $p_{n+1}$, he does so. Otherwise, he walks two units straight ahead to reach $p_{n+1}$. Using this modified rule, determine Aaron's position $p_{100}$.
A) $(22, 6)$
B) $(-22, 6)$
C) $(22, -6)$
D) $(-22, -6)$

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