
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 part of an "n-pointed regular star" is described, which is a simple closed polygon where all $2n$ edges are congruent, and alternate angles $A_1,A_2,\cdots,A_n$ and $B_1,B_2,\cdots,B_n$ at consecutive vertices are congruent respectively. If the acute angle at each $A_i$ is $20^\circ$ less than the acute angle at each $B_i$, compute the value of $n$ where $n$ is a natural number that ensures all angles between connecting edges total $360^\circ$ externally.
A) 12
B) 18
C) 24
D) 36
E) 60

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