
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 \( x \) and \( y \) be non-negative real numbers,
$$
a = \sqrt{x} + \sqrt{y}, \quad b = \sqrt{x+2} + \sqrt{y+2}.
$$

If \( a \) and \( b \) are two non-consecutive integers, find the values of \( a \) and \( b \).

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