
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
In a new scenario, Aaron the ant starts his journey at the origin $p_0=(0,0)$ on the coordinate plane, but instead of increasing his steps by 1 in the subsequent laps, he now increases by 2 each time he completes a full lap in the spiral pattern. For `n=1,2,3,...`, Aaron turns $90^\circ$ left and walks a number of steps to an unvisited point $p_{n+1}` unless that point is already visited, in which case he continues straight. His pattern of steps starts from 1 step for each direction on the first full cycle, but each subsequent cycle increases the steps for each direction by 2 from the previous cycle (e.g. the second cycle will have 3 steps in each direction, the third will have 5, and so on). Determine Aaron’s position at $p_{2024}$.
A) (23, 0)
B) (13, 0)
C) (-22, 13)
D) (0, 23)
E) (-22, -11)

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