
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:

$$
\begin{aligned}
(x+1)(3-4 y) & =(6 x+1)(3-2 y) \\
(4 x-1)(z+1) & =(x+1)(z-1) \\
(3-y)(z-2) & =(1-3 y)(z-6)
\end{aligned}
$$

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