
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
Given that \( n \) is a positive integer and \( a_{1}, a_{2}, \cdots, a_{n} \) are non-zero real numbers, define
$$
x = \frac{\left|a_{1} + a_{2}\right| + \left|a_{2} + a_{3}\right| + \cdots + \left|a_{n} + a_{1}\right|}{\left|a_{1}\right| + \left|a_{2}\right| + \cdots + \left|a_{n}\right|}
$$
Find the maximum and minimum values of \( x \).

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