
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
If $R$ is positive and the line whose equation is $x + y = 2R$ is tangent to the circle whose equation is $(x-1)^2 + y^2 = R$, determine the value of $R$.
A) $\frac{3 + \sqrt{5}}{4}$
B) $\frac{3 - \sqrt{5}}{4}$
C) $\sqrt{5}$
D) 2
E) $\frac{1}{2}$

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