
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 $a$ is positive and the line whose equation is $y = x + a$ is tangent to the circle whose equation is $(x - a)^2 + y^2 = a$, then $a$ equals?
- **A)** $\frac{1}{4}$
- **B)** $\frac{1}{3}$
- **C)** $\frac{1}{2}$
- **D)** $\frac{2}{3}$
- **E)** $1$

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