
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
All angles of an $n$-gon $A_{1} A_{2} A_{3} \ldots A_{n}$ are equal; and 

$$
A_{1} A_{2} \leqslant A_{2} A_{3} \leqslant A_{3} A_{4} \leqslant \ldots \leqslant A_{n-1} A_{n} \leqslant A_{n} A_{1} .
$$

What values can the ratio $\frac{A_{1} A_{n}}{A_{1} A_{2}}$ take?

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