
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
Suppose $g(t) = \frac{2t}{1-t}$, where $t \neq 1$. If $z = g(y)$, find the expression of $y$ in terms of $z$.
A) $g\left(\frac{1}{z}\right)$
B) $g\left(-z\right)$
C) $\frac{z}{2+z}$
D) $-g\left(-z\right)$
E) $-g\left(\frac{1}{z}\right)$

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