
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
Consider the equation $\dfrac{x+2y}{2y+3z} = \dfrac{3z+4w}{4w+x}$. Find the relation between variables that must hold.
A) $x = 3z$  
B) $x + 2y + 4w + 3z = 0$  
C) Either $x = 3z$ or $x + 2y + 4w + 3z = 0$, or both  
D) $x + 2y + 4w + 3z \neq 0$ if $x = 3z$  
E) $x(2y + 4w + 3z) = 3z(2y + 4w + x)$

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