
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:

$$
\begin{aligned}
& \frac{6}{3x + 4y} + \frac{4}{5x - 4z} = \frac{7}{12} \\
& \frac{9}{4y + 3z} - \frac{4}{3x + 4y} = \frac{1}{3} \\
& \frac{2}{5x - 4z} + \frac{6}{4y + 3z} = \frac{1}{2}
\end{aligned}
$$

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