
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
Round each term in the following expressions to $n=1, 2, 3, \ldots$ decimal places, and find the largest value of $n$ for which the rounded values of $K_{1}$ and $K_{2}$ are still equal. Also, consider the case when the terms are rounded to the nearest one, ten, hundred, and thousand.

$$
K_{1}=1842 \sqrt{2}+863 \sqrt{7}, \quad K_{2}=3519+559 \sqrt{6}
$$

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