
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, the real number \( x \) satisfies
$$
|1 - | 2 - |3 - \cdots |(n-1) - |n - x||\cdots||| = x.
$$

Determine the value of \( x \).

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