
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
Solve the following system of equations (where $a$ and $b$ are given):

$$
\begin{aligned}
\frac{a x+z}{y-z} & =\frac{1+b}{1-b} \\
\frac{2 a x-3 b}{2 y-3 z} & =1 \\
\frac{5 z-4 b}{3 a^{2} x-2 a y} & =\frac{b}{a}.
\end{aligned}
$$

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