
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
Let $n \in \mathbb{N}^*$, then calculate the value of $\sqrt{\overbrace{11\ldots1}^{2n\text{ digits}} - \underbrace{22\ldots2}_{n\text{ digits}}}$

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