
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
In an arbitrary numbering system, if the digits of a number \( N \) are:

$$
1,2,3, \ldots n, n-1, n-2, \ldots 3,2,1
$$

then \(\sqrt{N}\) is a number with \( n \) digits, each of which is 1.

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