
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
Let $f$ be a function defined by $f\left(\dfrac{x}{4}\right) = 2x^2 - 3x + 5$. Find the sum of all values of $z$ for which $f(4z) = 9$.
A) $\frac{3}{32}$  
B) $\frac{3}{64}$  
C) $\frac{1}{32}$  
D) $\frac{1}{64}$

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