
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's consider the circle represented by the equation $x^2 + y^2 = r^2$ and the line given by $x + y = r + 1$. Find the value of $r$ such that the circle is tangent to the line.
A) $\sqrt{2} - 1$  
B) $\frac{1}{\sqrt{2}}$  
C) $\sqrt{2} + 1$  
D) $\frac{1 + \sqrt{2}}{2}$  
E) $2$

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