
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
Given that the complex number $z$ satisfies the equation $$\frac{1+2z}{1-z} = i$$, find the value of $z$.

A) $$\frac{1}{5} + \frac{3}{5}i$$
B) $$\frac{1}{5} - \frac{3}{5}i$$
C) $$-\frac{1}{5} + \frac{3}{5}i$$
D) $$-\frac{1}{5} - \frac{3}{5}i$$

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