
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 20-step path is to go from (-5,-2) to (3,8) 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 rectangle $0 \le x \le 5$, $3 \le y \le 5$ at each step?

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