
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
Given that \( x, y, z \) are non-negative real numbers satisfying the equation
\[ 4^{\sqrt{5x + 9y + 4z}} - 68 \times 2^{\sqrt{5x + 9y + 4z}} + 256 = 0, \]
find the product of the maximum and minimum values of \( x + y + z \).

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