
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
Find $y$ in terms of $x$ given that $y = \sqrt{(x-2)^2} + \sqrt{(x^2 + 4x + 5)}$.
A) $ \sqrt{(x-2)^2} + (x+2)^2 $
B) $ |x-2| + \sqrt{(x+2)^2} $
C) $ |x-2| + \sqrt{(x+2)^2 + 1} $
D) $ |x-2| + |x+2| + 1 $

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