
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 24-step path is to go from $(-6,-6)$ to $(6,6)$ with each step increasing either the $x$-coordinate or the $y$-coordinate by 1. How many such paths stay outside or on the boundary of the square $-3 \le x \le 3$, $-3 \le y \le 3$ at each step?
A) 10,000  
B) 13,106  
C) 15,486  
D) 20,000  
E) 26,212

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