
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
[Point](https://artofproblemsolving.com/wiki/index.php/Point) $B$ is in the exterior of the [regular](https://artofproblemsolving.com/wiki/index.php/Regular_polygon) $n$-sided polygon $A_1A_2\cdots A_n$, and $A_1A_2B$ is an [equilateral triangle](https://artofproblemsolving.com/wiki/index.php/Equilateral_triangle). What is the largest value of $n$ for which $A_1$, $A_n$, and $B$ are consecutive vertices of a regular polygon?

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